Transformations. Name: Period:
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1 Transformations Name: Period:
2 2 Figures: Similar and ongruent 2 figures on the coordinate plane are either similar or congruent. Similar Figures ongruent Figures ~ Shapes are the same Shapes are the same Size is different Size is the same ~ Same angle measures orresponding sides are proportional Same angle measures Same corresponding side lengths Examples: 1. Explain why is congruent to EF. 2. Explain why is similar to EF.
3 SP: Similar and ongruent Figures 1. Which of the following statements about congruent figures are true? Select all that apply. The shape of the figures do not change The size of the figures do not change The coordinates of the figures do not change The angle measures of the figures do not change The side lengths of the figures do not change 2. Explain why is congruent to EF. 3. Explain why TUV is similar to QRS. 4. Which of the following statements about similar figures are true? Select all that apply. The shape of the figures do not change The size of the figures do not change The coordinates of the figures do not change The angle measures of the figures do not change The side lengths of the figures do not change
4 Slope Triangles Earlier this year, we used slope triangles to find the slope of a line. Ex: Find the slope of the line. We later recognized that the slope of a straight line is constant. Therefore, the slope of the line would be the same between any two given points on the line. Ex: Use the slope triangles provided to find the slope of the line at two different places. Slope 1: Slope 2: This is true because slope triangles on the same line will always be similar. Since similar shapes are proportional to each other, the ratio of the height over the width will simplify to the same ratio for both triangles. If you can show that the proportion exists, you can prove that the two triangles are similar.
5 Example: Prove that is similar to EF. F E SP: Similar and ongruent Figures 1. Prove that is similar to EF. F E 2. Prove that is similar to E. E
6 Translations: Graph & Ordered Pairs Translate each figure. Then determine if the figures are congruent or similar. Explain 1. 8 units right, 6 units down re the preimage and image congruent or similar? Explain. Translation Notation: 1. Translate 3 units right, 2 units up (4, 3), (2, 0), (5, 1) re the preimage and image congruent or similar? Explain. 2. Translate 3 units left, 2 units up S(0, 1), T(-2, -4), V(-3, 4), W(3, -2) re the preimage and image congruent or similar? Explain.
7 SP: Translations Transform each figure. Then determine if the figures are congruent or similar. Explain 1. 3 units left, 7 units up re the preimage and image congruent or similar? Explain. X Y 2. Translate 6 units left, 2 units up F(-5, 8), G(-3, 4), H(-8, 1), I(1, 6) re the preimage and image congruent or similar? Explain units left, 4 units down re the preimage and image congruent or similar? Explain. F G 4. What is the translation? J(-3, 4), K(-2, 1), L(-1, 3) J (1, -4), K (2,-7), L (3, -5) re the preimage and image congruent or similar? Explain.
8 Rotations: Graph & Ordered Pairs Rotate each figure. Then determine if the figures are congruent or similar. Explain. 90 clockwise or 270 counterclockwise around the origin (x, y) (, ) (2, 9) (2, 3) (7, 3) (7, 9) 180 clockwise or 180 counterclockwise around the origin (x, y) (, ) (2, 9) (2, 3) (7, 3) (7, 9) 270 clockwise or 90 counterclockwise around the origin (x, y) (, ) (2, 9) (2, 3) (7, 3) (7, 9)
9 SP: Rotations Transform each figure. Then determine if the figures are congruent or similar. Explain. 1. Rotate 180 counterclockwise around the origin 2. Rotate 270 clockwise around the origin X Z Y K L M 3. Rotate 180 clockwise around the origin 4. Rotate 90 clockwise around the origin W X Z Y R Q escribe the rotation. Then determine if the figures are congruent or similar. Explain. 5. T(5, 9) T (-9, 5) U(3, 7) U (-7, 3) V(1, 4) V (-4, 1) 6. L(-2, -4) L (2, 4) M(-1, -8) M (1, 8) N(-4, -1) N (4, 1) P(-6, -2) P (6, 2) 7. (-3, 6) (6, 3) (-5, 2) (2, 5) (-7, 5) (5, 7)
10 Reflections: Graph & Ordered Pairs Reflect each figure. Then determine if the figures are congruent or similar. Explain. Over the x-axis Over the y-axis Reflect over a line (not an axis) Reflect over x = 1 E Steps: 1. raw your line of reflection 2. ount each point of the preimage to the line of reflection. 3. ount the same distance to begin forming the image.
11 SP: Reflections Transform each figure. Then determine if the figures are congruent or similar. Explain. 1. Reflect over x = Reflect over the x-axis V T S W 3. Reflect over the y-axis 4. Reflect over x = 1 W Z Y L M X N escribe the reflection. Then determine if the figures are congruent or similar. Explain. 5. G(-7, 13) G (7, 13) H(-10, 8) H (10, 8) I(-1, 11) I (1, 11) 6. K(0, 3) K (0, 3) H(5, 3) H (-5, 3) 7. Q(4, 9) Q (4, -9) R(2, 6) R (2, -6) S(7, 3) S (7, -3)
12 ilations: Graph & Ordered Pairs The scale factor is the number that multiplies the preimage to determine the size of the new image. Enlarge: The scale factor is greater than 1 Reduce: The scale factor is between 0 and 1 No hange: Scale factor = 1 1. Scale Factor: 3 2. Scale Factor: 1 2 X W E G Y re the preimage and image congruent or similar? Explain. re the preimage and image congruent or similar? Explain. State the ordered pairs of the image after the given dilation. Then determine if the preimage and imare are congruent or similar. Explain. 3. Scale Factor = 4 4. Scale Factor = 1 9 X( 7, 13) X (9, 0) Y( 10, 8) Y (27, 9) Z( 1, 11) Z (45, 9)
13 SP: ilations Transform each figure. Then determine if the figures are congruent or similar. Explain. 1. Scale Factor: 2 2. Scale Factor: 1 3 W P N R Q T re the preimage and image congruent or similar? Explain. re the preimage and image conguent or similar? Explain. State the ordered pairs of the image after the given dilation. Then determine if the preimage and imare are congruent or similar. Explain. 3. Scale Factor = 6 4. Scale Factor = 1 5 N(2, 3) N K(-25, 35) K M(4, -2) M H(-5, 0) H J(2, 6) J F(30, 20) F 5. The Scale Factor is: X(2, 7) X (14, 49) Y(3, 2) Y (21, 14) Z(0, 9) Z (0, 63) 6. The Scale Factor is: (1, 7) (1, 7) (2, 3) (2, 3) (7, 6) (7, 6)
14 Sequence of Transformations 1. Use the sequence of transformations below when responding with details. Graph 1 Graph 2 Graph 3 W W a. escribe the sequence for each transformation. b. Is the preimage in Graph 1 and final image in Graph 3 similar or congruent? Explain. W 2. Use the sequence of transformations below when responding with details. F F Graph 1 Graph 2 Graph 3 F a. escribe the sequence for each transformation. b. Is the preimage in Graph 1 and final image in Graph 3 similar or congruent? Explain.
15 Sequence of Transformations 3. Z a. escribe the sequence for each transformation. Y X X X Y Y Z Z b. Is the preimage and final image similar or congruent? Explain. 4. Triangle JKL is shown on the coordinate plane. L Triangle JKL is rotated 90 clockwise about the origin to create J K L (not shown). Then J K L is reflected across the y-axis to create J K L (not shown). K What are the signs of the coordinates (x,y) of point K? J a) oth x and y are positive b) x is positive, y is negative c) oth x and y are negative d) x is negative, y is positive What are the signs of the coordinates (x,y) of point J? a) oth x and y are positive b) x is positive, y is negative c) oth x and y are negative d) x is negative, y is positive
16 Transformations General Understanding 1. What type of transformation creates similar figures? 2. What makes figures similar verses congruent? 3. If a preimage is dilated and the image is smaller than the preimage, what do you know about the dilation? 4. If a preimage is dilated and the image is larger than the preimage, what do you know about the dilation? 5. Fill in the table by checking the boxes that apply for each transformation. haracteristic Translations Rotations Reflections ilations The shape does not change The size of the shape does not change The orientation does not change The coordinates do not change reates congruent figures
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