ACTIVITY: Frieze Patterns and Reflections. a. Is the frieze pattern a reflection of itself when folded horizontally? Explain.
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1 . Reflections frieze pattern? How can ou use reflections to classif a Reflection When ou look at a mountain b a lake, ou can see the reflection, or mirror image, of the mountain in the lake. If ou fold the photo on its ais, the mountain and its reflection will align. Actual mountain Ais Reflection of mountain Frieze A frieze is a horizontal band that runs at the top of a building. A frieze is often decorated with a design that repeats. All frieze patterns are translations of themselves. Some frieze patterns are reflections of themselves. ACTIVITY: Frieze Patterns and Reflections Work with a partner. Consider the frieze pattern shown. COMMON CORE Geometr In this lesson, ou will identif reflections. reflect figures in the -ais or the -ais of the coordinate plane. Learning Standards 8.G. 8.G. 8.G. a. Is the frieze pattern a reflection of itself when folded horizontall? Eplain. b. Is the frieze pattern a reflection of itself when folded verticall? Eplain. 5 Chapter Transformations
2 ACTIVITY: Frieze Patterns and Reflections Work with a partner. Is the frieze pattern a reflection of itself when folded horizontall, verticall, or neither? a. b. ACTIVITY: Reflecting in the Coordinate Plane Math Practice Look for Patterns What do ou notice about the vertices of the original figure and the image? How does this help ou determine whether the figures are congruent? Work with a partner. a. Draw a rectangle in Quadrant I of a coordinate plane. Find the dimensions of the rectangle. b. Cop the aes and the rectangle onto a piece of transparent paper. Flip the transparent paper once so that the rectangle is in Quadrant IV. Then align the origin and the aes with the coordinate plane. Draw the new figure in the coordinate plane. List the vertices. c. Compare the dimensions and the angle measures of the new figure to those of the original rectangle. d. Are the opposite sides of the new figure still parallel? Eplain. e. Can ou conclude that the two figures are congruent? Eplain. f. Flip the transparent paper so that the original rectangle is in Quadrant II. Draw the new figure in the coordinate plane. List the vertices. Then repeat parts (c) (e). g. Compare our results with those of other students in our class. Do ou think the results are true for an tpe of figure?. IN YOUR OWN WORDS How can ou use reflections to classif a frieze pattern? Use what ou learned about reflections to complete Eercises 6 on page 58. Section. Reflections 55
3 . Lesson Lesson Tutorials Ke Vocabular reflection, p. 56 line of reflection, p. 56 A reflection, or flip, is a transformation in which a figure is reflected in a line called the line of reflection. A reflection creates a mirror image of the original figure. Line of reflection Flip EXAMPLE Identifing a Reflection Tell whether the blue figure is a reflection of the red figure. a. b. The red figure can be flipped to form the blue figure. So, the blue figure is a reflection of the red figure. If the red figure were flipped, it would point to the left. So, the blue figure is not a reflection of the red figure. Eercises 9 Tell whether the blue figure is a reflection of the red figure. Eplain.... Reflections in the Coordinate Plane Words To reflect a figure in the -ais, take the opposite of the -coordinate. To reflect a figure in the -ais, take the opposite of the -coordinate. Algebra Reflection in -ais: (, ) (, ) Reflection in -ais: (, ) (, ) B A C C A A B O C B In a reflection, the original figure and its image are congruent. 56 Chapter Transformations
4 EXAMPLE Reflecting a Figure in the -ais The vertices of a triangle are A(, ), B(, ), and C(6, ). Draw the figure and its reflection in the -ais. What are the coordinates of the image? Point A is unit above the -ais. B C Points B and C are units above the -ais. Plot point A unit below the -ais. A O 5 6 A C B Plot points B and C units below the -ais. Connect the vertices. The coordinates of the image are A (, ), B (, ), and C (6, ). EXAMPLE Reflecting a Figure in the -ais The vertices of a quadrilateral are P(, 5), Q(, ), R(, ), and S(, ). Draw the figure and its reflection in the -ais. Take the opposite of the -coordinate. The -coordinate does not change. Vertices of PQRS (, ) Vertices of P Q R S P(, 5) ( ( ), 5) P (, 5) Q(, ) ( ( ), ) Q (, ) S R P 6 5 P S R R(, ) ( ( ), ) R (, ) S(, ) ( ( ), ) S (, ) O Q Q The figure and its image are shown at the above right. Eercises 0 7. The vertices of a rectangle are A(, ), B(, ), C(, ), and D(, ). a. Draw the figure and its reflection in the -ais. b. Draw the figure and its reflection in the -ais. c. Are the images in parts (a) and (b) congruent? Eplain. Section. Reflections 57
5 . Eercises Help with Homework. WHICH ONE DOESN T BELONG? Which transformation does not belong with the other three? Eplain our reasoning.. WRITING How can ou tell when one figure is a reflection of another figure?. REASONING A figure lies entirel in Quadrant I. The figure is reflected in the -ais. In which quadrant is the image? 9+(-6)= +(-)= +(-9)= 9+(-)= Tell whether the blue figure is a reflection of the red figure Draw the figure and its reflection in the -ais. Identif the coordinates of the image. 0. A(, ), B(, ), C(, ). M(, ), N(0, ), P(, ). H(, ), J(, ), K(6, ), L(5, ). D(, ), E(0, ), F(0, 5), G(, 5) Draw the figure and its reflection in the -ais. Identif the coordinates of the image.. Q(, ), R(, ), S(, ) 5. T(, ), U(, ), V(6, ) 6. W(, ), X(5, ), Y(5, 5), Z(, ) 7. J(, ), K(7, ), L(9, ), M(, ) 8. ALPHABET Which letters look the same when reflected in the line? 58 Chapter Transformations
6 The coordinates of a point and its image are given. Is the reflection in the -ais or -ais? 9. (, ) (, ) 0. (, ) (, ). (, 5) (, 5). (, ) (, ) Find the coordinates of the figure after the transformations.. Translate the triangle unit right and 5 units down. Then reflect the image in the -ais.. Reflect the trapezoid in the -ais. Then translate the trapezoid units left and units up. S R T O X O Y W Z 5. REASONING In Eercises and, is the original figure congruent to the final image? Eplain. 6. NUMBER SENSE You reflect a point (, ) in the -ais, and then in the -ais. What are the coordinates of the final image? 7. EMERGENCY VEHICLE Hold a mirror to the left side of the photo of the vehicle. a. What word do ou see in the mirror? b. Wh do ou think it is written that wa on the front of the vehicle? F E 8. Reflect the triangle in the line =. How are the - and -coordinates of the image related to the - and -coordinates of the original triangle? D Classif the angle as acute, right, obtuse, or straight. (Skills Review Handbook) MULTIPLE CHOICE 6 is 75% of what number? (Skills Review Handbook) A 7 B 8 C 5 D 6 Section. Reflections 59
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