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Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor. 12 11 10 9. 8 D C ЕЗ -12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1. 1 2 3 4 5 6 7 8 9 10 11 12 R -5 -6 -8 Q -9 -10 -11

Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor. 12 11 10 9. 8 D C ЕЗ -12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1. 1 2 3 4 5 6 7 8 9 10 11 12 R -5 -6 -8 Q -9 -10 -11

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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## Educational Website: Geometry Concepts ### Understanding Congruence and Similarity through Rigid Motions and Dilations #### Diagram Description The provided image contains a coordinate plane with two figures: PQRTS and ABCDE. The coordinates of the points are plotted on a grid that spans from -12 to 12 on both the x- and y-axes. - **Figure PQRTS** is a pentagon oriented around the origin and includes the points: - \(P(-5, -8)\) - \(Q(4, -8)\) - \(R(4, -5)\) - \(S(2, -5)\) - \(T(0, -6)\) - **Figure ABCDE** is aligned horizontally near the top of the grid, with points along the y-axis at \(y = 0\): - \(A(6, 0)\) - \(B(-9, 0)\) - \(C(-6, 4)\) - \(D(6, 4)\) - \(E(9, 0)\) #### Detailed Analysis The task is to determine the relationship between figures PQRTS and ABCDE in terms of congruence and similarity by analyzing their properties and how they can be mapped onto each other using transformations. 1. **Congruence Analysis** - **Rigid Motions**: To determine if figure PQRTS is congruent to figure ABCDE, we need to check if a series of rigid transformations (translations, rotations, reflections) could map PQRTS exactly onto ABCDE. 2. **Similarity Analysis** - **Dilations and Rigid Motions**: To determine if figure PQRTS is similar to figure ABCDE, we need to see if a combination of dilations (resizing) and rigid motions can map PQRTS onto ABCDE. #### Questions for Students 1. **Congruence Check**: - Is figure PQRTS congruent to figure ABCDE because rigid motions [can/cannot] be used to map figure PQRTS onto figure ABCDE? [Options: can, cannot] 2. **Similarity Check**: - Is figure PQRTS similar to figure ABCDE because rigid motions and/or dilations [can/cannot] be used to map figure PQRTS onto figure ABCDE? [Options:
Transcribed Image Text:## Educational Website: Geometry Concepts ### Understanding Congruence and Similarity through Rigid Motions and Dilations #### Diagram Description The provided image contains a coordinate plane with two figures: PQRTS and ABCDE. The coordinates of the points are plotted on a grid that spans from -12 to 12 on both the x- and y-axes. - **Figure PQRTS** is a pentagon oriented around the origin and includes the points: - \(P(-5, -8)\) - \(Q(4, -8)\) - \(R(4, -5)\) - \(S(2, -5)\) - \(T(0, -6)\) - **Figure ABCDE** is aligned horizontally near the top of the grid, with points along the y-axis at \(y = 0\): - \(A(6, 0)\) - \(B(-9, 0)\) - \(C(-6, 4)\) - \(D(6, 4)\) - \(E(9, 0)\) #### Detailed Analysis The task is to determine the relationship between figures PQRTS and ABCDE in terms of congruence and similarity by analyzing their properties and how they can be mapped onto each other using transformations. 1. **Congruence Analysis** - **Rigid Motions**: To determine if figure PQRTS is congruent to figure ABCDE, we need to check if a series of rigid transformations (translations, rotations, reflections) could map PQRTS exactly onto ABCDE. 2. **Similarity Analysis** - **Dilations and Rigid Motions**: To determine if figure PQRTS is similar to figure ABCDE, we need to see if a combination of dilations (resizing) and rigid motions can map PQRTS onto ABCDE. #### Questions for Students 1. **Congruence Check**: - Is figure PQRTS congruent to figure ABCDE because rigid motions [can/cannot] be used to map figure PQRTS onto figure ABCDE? [Options: can, cannot] 2. **Similarity Check**: - Is figure PQRTS similar to figure ABCDE because rigid motions and/or dilations [can/cannot] be used to map figure PQRTS onto figure ABCDE? [Options:
**Congruence and Similarity of Figures** *Instructions:* Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor. *Graph Description:* The diagram features two quadrilaterals plotted on the coordinate plane with points labeled as follows: 1. **Quadrilateral ABCD** - A: (0, 0) - B: (-9, 0) - C: (-9, 6) - D: (0, 4) 2. **Quadrilateral PQRS** - P: (1, -6) - Q: (5, -6) - R: (4, -4) - S: (0, -4) *Detailed Explanation of Graph:* - The X-axis ranges from -12 to 12. - The Y-axis ranges from -12 to 12. - Both quadrilaterals have their vertices connected to outline their shapes. *Analysis Task:* 1. **Determine Congruence or Similarity:** - Congruent figures are identical in shape and size. - Similar figures have the same shape but differ in size. - Neither applies if the figures do not exhibit either characteristic. 2. **Calculate Scale Factor:** - If figures are determined to be similar, identify the ratio of corresponding side lengths to find the scale factor. *Observations:* - Examine corresponding vertices of quadrilateral ABCD and quadrilateral PQRS. - Compare corresponding distances to observe any proportional relationships or identical matches.
Transcribed Image Text:**Congruence and Similarity of Figures** *Instructions:* Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor. *Graph Description:* The diagram features two quadrilaterals plotted on the coordinate plane with points labeled as follows: 1. **Quadrilateral ABCD** - A: (0, 0) - B: (-9, 0) - C: (-9, 6) - D: (0, 4) 2. **Quadrilateral PQRS** - P: (1, -6) - Q: (5, -6) - R: (4, -4) - S: (0, -4) *Detailed Explanation of Graph:* - The X-axis ranges from -12 to 12. - The Y-axis ranges from -12 to 12. - Both quadrilaterals have their vertices connected to outline their shapes. *Analysis Task:* 1. **Determine Congruence or Similarity:** - Congruent figures are identical in shape and size. - Similar figures have the same shape but differ in size. - Neither applies if the figures do not exhibit either characteristic. 2. **Calculate Scale Factor:** - If figures are determined to be similar, identify the ratio of corresponding side lengths to find the scale factor. *Observations:* - Examine corresponding vertices of quadrilateral ABCD and quadrilateral PQRS. - Compare corresponding distances to observe any proportional relationships or identical matches.
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