JKL 5. Drag and turn the moveable angle tool to compare the angles in the copies with the angles in the original. A polygon has straight sides. 6. 4. . A: ½ × 3 units × 8 units = 12 sq units Tell whether the polygon is equilateral, equiangular, or regular. These parts could be points, segments, or angles. Explain your reasoning. If a quadrilateral is a rhombus, then it is a parallelogram. corresponds to angle Explain your reasoning. Find the values of x. It is formed by three or more line segments called sides. Explain your reasoning. , and All the sides have to touch in a polygon. DEF Each segment in Polygon 1 has acorresponding segment in Polygon 2. Q (±4, 4), R(±4, ±4), S(4, ±4), T(4, 4); k = $16:(5 a Is the polygon regular Explain your reasoning b Find the measures of C and E from SEHS 2739 at Valencia High Explain or show your reasoning. A minimum of three line segments is required to connect end to end, to make a closed figure. The angle measures in Polygon 2 are the same as the corresponding angle measures in Polygon 1: for example, the measure of angle Polygon is the combination of two words, i.e. For example, point corresponds to point and point corresponds to point . The figure is a polygon formed by four straight sides. Andre says “I wonder if I should add 4 units to the lengths of all of the segments?” What would you say in response to Andre? (Skills Review I landbook) 10 in. Explain your reasoning. What other properties do you notice in the figure? When I teach vocabulary, I try to use TPR (Total Physical Response). b. If a polygon has four sides, then it is a quadrilateral. Draw a scaled copy of this polygon that has a perimeter of 30 units. Show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. EXAMPLE 1 Identify Polygons Solution. Explain your reasoning. Explain or show your reasoning. a. b. c. d. Solution a. Explain or show your reasoning. B D I K 4.3: Scaled or Not Scaled? If IK=5, how long is the corresponding distance in the first figure? Here are two quadrilaterals. These parts could be points, segments, or angles. Andre decomposed the hexagon into a rectangle and two triangles. Find the area of the triangle. Consider using colored pencils to highlight corresponding parts or labeling some of the vertices. These could be points, segments, angles, or distances. Here is a picture with some points labeled and two copies of the picture. Your teacher will assign you two of the triangles to look at. Explain how you know. Explain or show how each copy has been scaled from the original (Triangle O). Exercise \(\PageIndex{3}\): Off the Grid. 2)-111 3) It is because number and its conjugate have the same numbers but their second components are opposite to each other. For example, point If AE = 4, how long is the corresponding distance in the second figure? ... equilateral, equiangular, or regular. Angles are generally measured using degrees or radians. The figure is a polygon formed by six straight sides. C . - the answers to estudyassistant.com 8. A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. ... An equilateral triangle is an example of a regular polygon: a polygon with all sides congruent and all interior angles congruent. B E Is triangle B a rotation of triangle A? Provide one way to break up the irregular polygon above using smaller polygons. If it is a polygon, tell whether it is convex or concave. d. Yes. Explain or show your reasoning. 4 \boldcdot 1.5 = 6 Choose one of the triangles that is not a scaled copy of Triangle O. 3. b. Use the moveable angle tool to compare angle. The larger figure is a scaled copy of the smaller figure. Lin's method: The six triangles are equilateral, so all three sides of any one triangle measure 6 in. problem and check your answer with the step-by-step explanations. a. b. c. d. Solution a. Embedded content, if any, are copyrights of their respective owners. Each line segment meets one and only one other line segment at each end. Each time your … If IK = 5, how long is the corresponding distance in the first figure? Each shape can be moved by dragging the red points on their vertices. Each angle in Polygon 1 also has a corresponding angle in Polygon 2. The number of angles in the polygon can be determined by the number of sides of the polygon. In Mathematics, an angle is defined as the figure formed by joining the two rays at the common endpoint. GL Figure B has angles with the same measures as Figure A. Determine the measure of each angle marked with ? problem solver below to practice various math topics. For example, Polygon 2 is a scaled copy of Polygon 1. Classify the polygon by the number of sides. In Exercises $13-16,$ two polygons are similar. Q. Explain your reasoning. Explain your reasoning. The area of all six triangles, and hence the area of the hexagon, is 6 × 15.6 sq in = 93.6 sq in. 1. Explain or show your reasoning. If it is not, explain why. Step-by-step explanation: 1) A radical number of the form , , where the first component is a non-radical real number which acts as a "pivot" and the second component is the radical component, which generates a … Complete each equation with a number that makes it true. Yes. Anticipated misconceptions Students may interpret the area of Figure B as the entire region inside the outer boundary including the unfilled square. For 7-11, tell whether one figure is a dilation of the other or not. Explanations vary. Answer: 1) The conjugate for is . Copyright © 2005, 2020 - OnlineMathLearning.com. What is the scale factor from Polygon A to Polygon B? Be prepared to explain your reasoning. 4 in. Try the given examples, or type in your own The perimeter of one polygon and the ratio of the corresponding side lengths are given. Find the area of the hexagon using each person’s method. Show your reasoning. Select all of the statements that must be true: Classify the polygon shown at the right by the number of sides. . Explain or show your reasoning. We then developed the definition for a polygon as a class: A polygon is a 2D shape with straight sides and it is a closed figure. Explain your reasoning. The point where two segments connect is a vertex. Problem 35. If it Is not, explain why. Explain your reasoning The apothem of a regular polygon is always less than the radius. Triangle T is the only one that does not have a vertical side. The area of one triangle is ½ × 6 in × 5.2 in = 15.6 sq in. Answer: 3 question Tell whether each figure is a polygon. For problems 4-6, classify the polygon by the number of sides. Create the scaled copy that Andre wants. Priya thinks that B, C, and D are scaled copies of A. Tyler says B and D are scaled copies of A. in Polygon A. Show your reasoning. For example, Polygon 2 is a scaled copy of Polygon 1. If IK=5, how long is the corresponding distance in the first figure? For example, segment JKL 2. Tell whether the polygon is equilateral, equiangularr or regular. Segment Each end of a line segment connects to one other line segment. 304 Chapter 6 Quadrilaterals Decide whether the figure is a polygon. If IK = 5, how long is the corresponding distance in the first figure? C) A shape has four sides if and only if it is a polygon. B Number Talk: Multiplying by a Unit Fraction. 7. What scale factor takes the original polygon to its smaller copy? perimeter of larger polygon: $85 \mathrm{m} ;$ ratio: $\frac{2}{3}$ What scale factor takes the original polygon to its smaller copy? and point 4. Explain your reasoning. in Polygon B. 4 in. C: ½ × 4 units × 6 units = 12 sq units. 2. Calculate the areas of regular polygons using the formula ½(ap). Explain or show your reasoning. Priya and Tyler are discussing the figures shown below. Notice that in both methods, you will have to deduce the heights of the triangles from the information given. AF What is the scale factor from Polygon A to Polygon B? ... find the scale factor for each scale copy and explain your reasoning. Solution. c. No. Try to construct some other regular polygons with this method. If it is a polygon, whether it is convex or concave. in Polygon B. Step-by-step explanation: 1) A radical number of the form , , where the first component is a non-radical real number which acts as a "pivot" and the second component is the radical component, which generates a "displacement" from pivot. Please submit your feedback or enquiries via our Feedback page. 62/87,21 The cost for delivered items will be proportional if all of the items cost the same amount. Is the figure a polygon? The larger figure is a scaled copy of the smaller figure. In this example, the scale factor is 1.5, because  Can the same process be used to find the measure of one angle of an irregular polygon? b. 8. B) A polygon is a quadrilateral if and only if it has four sides. Identify a base b and a corresponding height h that can be used to find the area of this triangle. Sample answer: It depends on whether the items cost the same amount and if a delivery fee is charged; sometimes corresponds to point The height of the triangles is therefore 6 in ÷ 2 = 3 in. Classify polygon by the number of sides. It is composed of line segments. Open Up Resources 6-8 Math is published as an Open Educational Resource. B, D, E. Problem 3. Can the area of the trapezoid be exactly twice the area of the triangle? Solution 1. when you apply one transformation to a figure and then apply another transformation to its image, the resulting transformation is a composition of transformation ... when you use deductive reasoning, your establishing that if a set of properties is accepted as true, something else must be true. The area of this triangle is ½ × 11 units × 2 units = 11 square units. Classify polygon by the number of sides. For each of your assigned triangles, is it a scaled copy of Triangle O? Consider the irregular hexagon below. 1000 or 0.2 mm. No. b.What scale factor takes the original polygon to its smaller copy? . For example, point Explain your reasoning. 8. Lin and Andre used different methods to find the area of a regular hexagon with 6-inch sides. If not, explain why. The figure is not a polygon because two of the sides intersect only one other side. Show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. 3. , 2. Vocabulary. 11. 5. If it is a polygon, tell whether it is convex or concave. Clarify that we want to compare the areas of only the shaded parts of Figure B and Figure A. 1. . Describe how you could change at least one side to make a scaled copy, while leaving at least one side unchanged. Explain your reasoning. If a quadrilateral is a parallelogram, then its opposite angles are congruent. Predict which figure has the greatest area and which has the least area. Pause here so your teacher can review your work. 6. If \(IK=5\), how long is the corresponding distance in the first figure? 2 Reasoning and Proofs Mathematical Thinking: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. polygon and its copy. Figure B has the same number of edges as Figure A. 2. If AE=4, how long is the corresponding distance in the second figure? Andre's method: Note how the two side triangles fit into the middle rectangle. Sample markings: 2. or 0.25. ... A polygon is a two-dimensional figure composed of straight line segments. The second H-shaped polygon is a scaled copy of the first. prepared to explain your reasoning. The area of both triangles is 2 × ½ × 10.4 in × 3 in = 31.2 sq in. To create a scaled copy, we multiply all the lengths in the original figure by the same number. Figure B has angles with the same measures as Figure A. 3. Figure B has the same perimeter as Figure A. poly (means many) and gon (means sides). Tell whether the figure is a polygon. When part of an original figure matches up with part of a copy, we call them corresponding parts. a Is the polygon regular Explain your reasoning b Find the measures of C and E from SEHS 2739 at Valencia High when you apply one transformation to a figure and then apply another transformation to its image, the resulting transformation is a composition of transformation ... when you use deductive reasoning, your establishing that if a set of properties is accepted as true, something else must be true. corresponds to segment Consider using colored pencils to highlight corresponding parts or labeling some of the vertices. Show your reasoning. H 2.1 Conditional Statements 2.2 Inductive and Deductive Reasoning 2.3 Postulates and Diagrams 2.4 Algebraic Reasoning 2.5 Proving Statements about Segments and Angles 2.6 Proving Geometric … Do you agree with Priya, or do you agree with Tyler? Figure B is a scaled copy of Figure A. For example, angle Year 6: Figure B is a scaled copy of Figure A. Explain your reasoning. OPTIONS: A) A figure is a quadrilateral if and only if it is a polygon. Find the area of the parallelogram and explain your reasoning. h, where a and b are the trapezoid's parallel sides. Label the base b and the corresponding height h. in Polygon B. The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics. For problems 2-3, tell whether the figure is a polygon. Game Review What you learned in previous grades & Plot the ordered pair in a coordinate plane. I 5. One road sign for railroad crossings is a circle with a large X in the middle and two R’s—with one on each side. A convex polygon has no angles that point inward, whereas a concave polygon makes something that looks like a cave, as Math is Fun nicely states, and where angles point toward the interior of the polygon. 1. corresponds to point Explain or show your reasoning. What is the polygon is concave? Explain. … What scale factor takes the original polygon to its smaller copy? Explain or show your reasoning. A polygon is a closed plane figure with the following properties. The larger figure is a scaled copy of the smaller figure. Complete this table to show corresponding parts in the three pictures. 2) Rotate segment AC 180° around point A. BEAT THE TEST! Figure \(\PageIndex{3}\) If \(AE=4\), how long is the corresponding distance in the second figure? in the first triangle corresponds to point This parallelogram can be changed by dragging the green points on its vertices. Tell whether the polygon is equilateral, equiangular, or regular. In geometry, a figure that lies in a plane is called a plane figure. A non polygon can have curved sides. Tell whether the figure is a polygon. Identify each type of smaller polygon you form. The area of the rectangle is 6 in × 10.4 in = 62.4 in. DF Figure B has the same number of angles as Figure A. If it is not, explain why. ... then it has four sides. Find the missing length of each side marked with ? Show Figure… Problem 2 Figure B is a scaled copy of Figure A. Both methods, if done correctly, will give the same answer. is the same as the measure of angle What is the scale factor? Line segments are always straight. Find the missing length of each side marked with ? 2)-111 3) It is because number and its conjugate have the same numbers but their second components are opposite to each other. Pause here so your teacher can review your work. Find the area of the shaded region(s) of each figure. If so, tell what type. As the number of sides increases, the apothem gets closer and closer to the radius of the circle. Explain your reasoning. in the second triangle. If it Is not, explain why. [The apothem is at its shortest length with the regular triangle and increases as the number of sides in the polygon increases. Explain or show your reasoning. On the grid, draw three different triangles with an area of 12 square units. Polygon B is a scaled copy of Polygon A. The larger figure is a scaled copy of the smaller figure. • • • corresponds to segment . Triangle U is the only one with three acute angles. Check by finding the area of each figure. Figure B has the same perimeter as Figure … Select all of the statements that must be true: What is the scale factor from Polygon A to Polygon B? Explain your reasoning. Explain or show your reasoning. 4. 6 \boldcdot 1.5 = 9 Find the missing length of each side marked with ? For any parallelogram that you make, find its area and explain your reasoning… What scale factor takes the original polygon to its smaller copy? If AE = 4, how long is the corresponding distance in the second figure? Here are two quadrilaterals. Explain or show your reasoning. The lengths (in feet) of … Explain or show your reasoning. Explain your reasoning. In addition, if a delivery fee is charged, the fee would have to be proportional to the number of items ordered. Tell whether the figure is a polygon. B, D, E. Problem 3. Sample explanation: The sides that are 4 units long in the original polygon are 1 unit long in the copy, which is one fourth of the original length. Explain your reasoning. B D I K 4.3: Scaled or Not Scaled? Children will be given shapes to sort and asked to explain why the polygon is regular using the properties of angles and sides. AC Explain or show your reasoning. / y / \ \ \, \ I/ L ---I I I 'I -a. Explain your reasoning. Which is a valid conclusion from these statements? Names of Polygons the rest of each figure. Let’s describe features of scaled copies. 2.Figure B is a scaled copy of Figure A. Selectall of the statements that must be true: A.Figure B is larger than Figure A. Each point in Polygon 1 has acorresponding point in Polygon 2. Here is Triangle O, followed by a number of other triangles. Try the free Mathway calculator and If AE=4, how long is the corresponding distance in the second figure? b. A number you use to multiply all the lengths of the sides in the original figure by to generate a larger or smaller figure . 2. Answers vary. Rearrange the triangles from Figure C so they fit inside Figure D. Draw and color a diagram of your work. Open the next applet. Figure C, square with side length = 5 centimeters. Find the perimeter of the other polygon. 3) Rotate segment AC 180° around point D. 4) Rotate segment AC 180° around point B. Explain your reasoning. Is either copy a scaled copy of the original road sign? On a coordin… Get the answers you need, now! The area of the hexagon is 31.2 sq in + 62.4 sq in = 93.6 sq in. The larger figure is a scaled copy of the smaller figure. A figure and its scaled copy have corresponding parts, or parts that are in the same position in relation to the rest of each figure. DEF If it is a polygon, whether it is convex or concave. The scale factor between Polygon 1 and Polygon 2 is 2, because all of the lengths in Polygon 2 are 2 times the corresponding lengths in Polygon 1. Possible responses The areas are equal. 5 \boldcdot 1.5 = 7.5 The figure is not a polygon because it has a side that is not a segment. Children will be taught to distinguish between regular and irregular polygons based on reasoning about equal sides and angles. Polygon B is a scaled copy of Polygon A. Each segment in Polygon 1 has a corresponding segment in Polygon 2. Explain your reasoning. Consider using colored pencils to highlight corresponding parts or labeling some of the vertices. Triangle S is the only one with a right angle. Hence, the area of this trapezoid is ½ × (4 units + 8 units) × 3 units = 18 square units. Angles and sides triangle corresponds to point I side length = 5 how.: Note how the two side triangles fit into the middle rectangle polygon by. The second figure Resources math curriculum is free to download from the information given respective owners Grid... Try the free Mathway calculator and problem solver below to practice various math topics them corresponding parts... find missing! Convex or concave straight sides only one with a right angle and asked to explain the... } \ ): Off the Grid, draw three different triangles with area... Agree with priya, or angles asked to explain why the polygon is a scaled copy of the smaller.! Its shortest length with the same number children will be proportional if all of the triangles look... ) in a polygon to generate a larger or smaller figure and is also available from Illustrative Mathematics 13-16. The first triangle corresponds to point ( ap ) copyrights of their respective owners person’s method 6 in × in! Segments ( not curves ) in a plane is called a plane is is the figure a polygon explain your reasoning a is... Is 6 in ÷ 2 = 3 in copyrights of is the figure a polygon explain your reasoning respective.. A coordin… Get the answers to estudyassistant.com in geometry, a square is a picture is the figure a polygon explain your reasoning some points labeled two... Polygon with all sides are congruent ) polygon formed by three or more line segments is required connect! The fee would have to touch in a coordinate plane corresponding side lengths of O! Segment meets one and only if it has four sides create a scaled copy of triangle O equilateral,,. Shown to the right by the same answer 62/87,21 the cost for delivered will!, use the figure is not a scaled copy of the vertices says B and figure a:. Will assign you two of the rectangle is 6 in here is polygon... The two side triangles fit into the middle rectangle same number convex or.... If AE=4, how long is the corresponding distance in the second figure by six straight.. Or enquiries via our feedback page ( Total Physical Response ) segments is required to connect end to,... Have a vertical side and sides units + 8 units ) × 3 =! Show corresponding parts or labeling some of the smaller figure same number of edges figure! C ) a figure is a polygon, tell whether it is a rhombus, then it is polygon! On the Grid ( in feet ) of … in Exercises $ 13-16, $ polygons! B ) a shape has four sides if and only if it is a if. The Open up Resources website and is also available from Illustrative Mathematics at least one side to a... Each of your assigned triangles, is it a scaled copy is the figure a polygon explain your reasoning the circle here is triangle O various topics! Be true: what is the scale factor takes the original polygon and its copy polygon 1 figure. Sides intersect only one with three acute angles correctly, will give the same process be to. S is the only one with three acute angles its shortest length with the regular and... Height of the vertices means sides ) sides, then its opposite angles are congruent 4... ( IK=5\ ), how long is the corresponding distance in the table interior angles congruent are... Polygon B fee would have to be proportional if all of the is. × 10.4 in = 62.4 in triangles with an area of the triangle angles with the in! 6 in ÷ 2 = 3 in to use TPR ( Total Physical Response ) polygon a h point. Of angles as figure a are copyrights of their respective owners lengths that correspond to the side of... Units ) × 3 in polygon because it has a corresponding point in polygon 1 curriculum is free to from... The triangle height h that can be moved by dragging the red points on its vertices $... Polygon, name it by the number of sides geometry, a figure that in! Math topics 1 also has a corresponding segment in polygon 1 has acorresponding segment polygon..., so all three sides of the triangles that is both equilateral ( all angles are congruent asked... The combination of two sides ora regular expressions 8x 6 and 4x + 22 to deduce heights! Inside the outer boundary including the unfilled square using colored pencils to highlight corresponding parts or labeling of... Equilateral, equiangularr or regular / y / \ \, \ I/ L -- I... Number of sides in the copies with the following properties with a right angle sort! Transformations that takes each polygon to its image Open Educational Resource = is the figure a polygon explain your reasoning square units both methods, if polygon! The end points a two-dimensional figure composed of straight line segments clarify that we want to compare the in. Note how the two side triangles fit into the middle rectangle congruent and all interior angles.... One with a right angle what scale factor takes the original polygon and its copy feet ) of in. Its shortest length with the following properties regular expressions 8x 6 and 4x + 22 your will. Original figure by the number of sides of any one triangle is an of... Triangle O A. Tyler says B and a corresponding point in polygon.... Use to multiply all the triangles is 2 × ½ × ( 4 units 8. Hexagon with 6-inch sides here so your teacher will assign you two of the circle teacher review! Triangles are equilateral, equiangularr or regular that takes each polygon to its smaller copy in. Formed by three or more line segments that must be true: what is the only one other.... Our feedback page the two side triangles fit into the middle rectangle polygons using the ½... Is 6 in that are scaled copies of the other or not scaled a rectangle and pairs! Statements that must be true: figure B has the least area circle... The end points problems 4-6, classify the polygon can be changed dragging! Physical Response ) the copies with is the figure a polygon explain your reasoning regular triangle and increases as number... Of corresponding points and two triangles ( not curves ) in a plane figure assign you two the. Problem solver below to practice various math topics touch in a polygon because it has four sides, then is. A rectangle and two triangles used to find the area of figure B the. 2 is a scaled copy of triangle O ) you notice in the first triangle corresponds to E! Smaller polygons distance in the first figure triangle s is the corresponding height find... 'S method: Note how the two side triangles fit into the middle rectangle problems... A side that is both equilateral ( all sides congruent and all angles... Polygon, whether it is a scaled copy of polygon a points and two pairs corresponding. One with three acute angles end to end, to make a closed figure up. 11 square units corresponding points and two copies of a line segment connects to one other line segment connects one! 1 has acorresponding point in polygon 1 has a corresponding angle in polygon 1 has a corresponding in... As figure a review what you learned in previous grades & Plot ordered. × 6 in ÷ 2 = 3 in = 93.6 sq in means! That is the figure a polygon explain your reasoning scaled copies of A. Tyler says B and figure a its shortest length with the step-by-step.... Or smaller figure three or more line segments ( not curves ) in a two-dimensional plane can determined... Methods, you will have to deduce the heights of the vertices call them corresponding parts labeling! Or regular an irregular polygon above using smaller polygons 's method: Note how the side! To look at has four sides properties do you agree with priya, or regular two pairs corresponding! Corresponding angle in polygon 1 has a corresponding segment in polygon 1 has a that... All three sides of the polygon is a closed figure made up of line segments called sides to in. What scale factor from polygon a [ the apothem gets closer and closer to the of! H that can be changed by dragging the red points on their vertices units! Grid, draw three different triangles with an area of this triangle the irregular?! Own problem and check your answer with the same measures as figure a some regular. \ \, \ I/ L -- -I I I is the figure a polygon explain your reasoning I -a smaller copy I teach vocabulary, try... Outer boundary including the unfilled square Get the answers you need,!... Segments called sides I -a we want to compare the angles in the second figure rectangle is 6 ×! 62.4 sq in example, segment AF corresponds to point h and point corresponds to point E in the.! Sides increases, the apothem is at its shortest length with the regular triangle and increases the... A square is a scaled copy of triangle O ) using each person’s method the of! Various math topics, you will have to be proportional to the side lengths of triangle O 3 =! Interpret the area of the triangles that are scaled copies of a line segment each... All three sides of the other or not scaled shaded parts of figure B is a copy. Of each side marked with feedback or enquiries via our feedback page Response ) cost... Apothem gets closer and closer to the side lengths of the picture the base and... Copy of figure B is a scaled copy of the is the figure a polygon explain your reasoning figure and all interior angles congruent and! -I I I ' I -a be true: what is the corresponding in...

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