Plot and connect the points in a coordinate plane to make a polygon. Name the polygon.

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1 . Start Thinking Find at least two objects in each of the following categories: circle, square, triangle, and rectangle (nonsquare). Use a table to compare each object of the same categor in the following was: re all angle measures the same? Is each shape eactl the same? re the objects the same size?. Warm Up Plot and connect the points in a coordinate plane to make a polgon. Name the polgon.. (, ), B(, ), (, ). E(, ), F(, ), G(, ), H(, ). J(, ), K(, ), L(, ), M(, ). P(,, ) Q(,, ) R(,, ) S(, ). umulative Review Warm Up Find the coordinates of point P along the directed line segment B so that P to PB is the given ratio.. ( ) B( ),, 9, ; to. ( ) B( ),,, 0; to. ( ) B( ),,, ; to. ( ) B( ),,, ; to

2 Name Date. Practice In Eercises and, identif an congruent figures in the coordinate plane. Eplain In Eercises and, describe a congruence transformation that maps B to B... B B B B In Eercises and, determine whether the polgons with the given vertices are congruent. Use transformations to eplain our reasoning.. (, ), B(, ), (, ) and S(, ), T(, ), U(, 0). E(, ), F( 0, ), G( 0, ), H(, ) and W(, ), X(, 0 ), Y(, 0 ), Z(, ). In the figure, a b, DE is reflected in line a, and DE is reflected in line b. List three pairs of segments that are parallel to each other. Then determine whether an segments are congruent to EE. In Eercises and 9, find the measure of the acute or right angle formed b intersecting lines so that P can be mapped to P using two reflections.. rotation of maps P to P. 9. The rotation ( ) ( ),, maps P to P. D D E E a b D E

3 Name Date. Practice B. Identif an congruent figures in the coordinate plane. Eplain.. Determine whether the polgons with the vertices ( 0, ), B(, ), (, ), D (, ) and P(, ), Q(, ), R(, ), S(, ) are congruent. Use transformations to eplain our reasoning. In Eercises, JKL is reflected in line a, and JKL is reflected in line b.. JK is perpendicular to line a and has a length of units, and verte K is unit from line a. Find the distance JJ.. Find the angle of rotation that maps JKL onto J KL.. Is JK parallel to J K? Eplain our reasoning.. The rotation (, ) (, ) maps P and P. Find the measure of the acute or right angle formed b intersecting lines so that P can be mapped to P using two reflections.. Is it alwas, sometimes, or never true that the composition of two reflections results in the same image as a translation? Eplain our reasoning. J a K J K L L 0 L b K J. is reflected in line s to form and then reflected in line t to form. Draw line t and intermediate to complete the figure that represents these transformations. s 9. Your friend claims that if ou have a series of man parallel lines, reflecting a figure in two of the lines will produce the same result as reflecting the image in four or si of the lines. Is our friend correct? Eplain our reasoning.

4 Name Date. Enrichment and Etension Matri ddition and Translation matri is a rectangular arrangement of numbers in rows and columns. (The plural of matri is matrices.) Each number in a matri is called an element. The dimensions of a matri are the numbers of rows and columns. The matri to the right has three rows and four columns, so the dimensions of the matri are, read three b four. 9 You can represent a figure in the coordinate plane using a matri with two rows. The first row has the -coordinates of the vertices. The second row has the corresponding -coordinates. Each column represents a verte, so the number of columns depends on the number of vertices of the figure. Eample: Write a matri to represent point D. Solution: The -coordinate is and the -coordinate is. D E. Write a matri to represent point F.. Write a polgon matri for DEFG. G F To add or subtract matrices, ou add or subtract corresponding elements, and the resulting matri must have the same dimensions. Perform the operation In Eercises, use the diagram.. Write a polgon matri for B.. Write a matri that, when added to the polgon matri for B, translates the coordinates unit left and units up. This matri is called a translation matri. B. dd the translation matri from Eercise to the polgon matri B. The result is called an image matri, which represents the sum of a translation matri and the matri of a preimage.. Graph a congruent triangle of B translated unit left and units up. Label the triangle B. What do ou notice about the resulting coordinates?

5 Name Date. Puzzle Time What Geometric Figure Is Like Lost Parrot? Write the letter of each answer in the bo containing the eercise number.. omplete the sentence. Two geometric figures are figures if and onl if there is a rigid motion or a composition of rigid motions that maps one of the figures onto the other.. ongruent figures have the same size and shape. True or false?. re three equilateral triangles with respective sides of centimeters, centimeters, and inches congruent? Yes or no?. figure is reflected in line k, and the image is then reflected in line m. The measure of the acute angle formed between lines k and m is. What is the angle of rotation? Given B with vertices (, ), B(, ), and (, ), and the, +,, find the verte of the image. translation ( ) ( ).. B.. omplete the sentence. The polgons with vertices ( 0, ), B( 0,, ) (,, ) D (, ) and E(, ), F(, 0 ), G (, 0 ), H (, ) congruent. nswers R. are not I. constructed N. (, ) M. es. are B. (, ) G. (, ) L. P. no E. O. true X. (, ) Y. congruent O. (, ) U. (, ) 9