S B. 10 ft. 5 ft. PearsonTEXAS.com. Property Line STEM. Property Line

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1 In each diagram, the blue figure is an image of the black figure. (a) hoose an angle or point from the preimage and name its image. (b) List all pairs of corresponding sides G W X. In the diagram at the right, the orange figure is a translation image of the red figure. Write a coordinate rule that describes the translation. 10. ispla athematical Ideas (1)(G) UG has coordinates (2, -4), U(6, 6), and G(7, 2). translation maps point to ( -, 6). What are the coordinates of U and G for this translation? 11. ustif athematical rguments (1)(G) L has vertices ( -2, 0), L( -1, 1), (0, 1), and ( -1, 0). he translation 62, -7 (L) = L. how that, LL,, and are all parallel. 12. nalze athematical elationships (1)() If 65, 77 ( O) = O, what coordinate rule maps O onto O? 1. ppl athematics (1)() he diagram at the right shows the site plan for a backard storage shed. Local law, however, requires the shed to sit at least ft from propert lines. escribe how to move the shed to compl with the law. 14. You write a computer animation program to help oung children learn the alphabet. he program draws a letter, erases the letter, and makes it reappear in a new location two times. he program uses the following composition of translations to move the letter. ropert Line 10 ft 5 ft ropert Line 65, 77 (, ) followed b 6-, -27 (, ) uppose the program makes the letter W b connecting the points (1, 2), (2, 0), (, 2), (4, 0) and (5, 2). What points does the program connect to make the last W?. onnect athematical Ideas (1)() has vertices ( -2, 5), ( -4, -1), and (2, -). If 64, 27 ( ) =, show that the images of the midpoints of the sides of are the midpoints of the sides of. 16. plain athematical Ideas (1)(G) plain how to use translations to draw a parallelogram. 17. Use the graph at the right. Write three different rules for which the image of L has a verte at the origin. 4 2 L 4 2 O 2 earsonx.com 2

2 roblem 4 What do ou have to know about GH to show that it is an isosceles triangle? Isosceles triangles have at least two congruent sides. Using roperties of eflections In the diagram, t (G) = G, t (H) =, and t () =. Use the properties of reflections to describe how ou know that GH is an isosceles triangle. ince t (G) = G, t (H) =, and reflections preserve distance, t (GH ) = G. o GH = G and, b definition, GH is an isosceles triangle. H G t OLI H O W O I and LIIO XI can page for a Virtual erd tutorial video. reate epresentations to ommunicate athematical Ideas (1)() Given points (1, 4), (, 5), and G(2, 1), graph G and its reflection image as indicated. or additional support when completing our homework, go to earsonx.com. 1. -ais 2. -ais. = 2 4. = 5 5. = = 2 7. ach figure in the diagram at the right is a reflection of another figure across one of the reflection lines. a. Write a reflection rule to describe igure. ustif our answer. j igure igure 4 b. Write a reflection rule to describe igure 2. ustif our answer. c. Write a reflection rule to describe igure 4. ustif our answer. igure 1 n igure 2. ppl athematics (1)() Give three eamples from everda life of objects or situations that show or use reflections.. In the diagram at the right, L is a rectangle with L = 2. a. op the diagram. hen sketch L (L). b. What figure results from the reflection? Use properties of reflections to justif our solution. op each pair of figures. hen draw the line of reflection ou can use to map one figure onto the other L earsonx.com 2

3 etermine whether the polgons are similar. If so, write a similarit statement and give the scale factor. If not, eplain G L he polgons are similar. ind the value of each variable z he space allowed for the mascot on a school s Web page is 120 piels wide b 0 piels high. Its digital image is 500 piels wide b 75 piels high. What is the largest image of the mascot that will fit on the Web page? In the diagram at the right, G H. ind each of the following. 11. m 12. G H G. nalze athematical elationships (1)() You want to make a scale drawing of ew York it s mpire tate uilding using the scale 1 in. = 250 ft. If the building is 1250 ft tall, how tall should ou make the building in our scale drawing? 16. he avis famil is planning to drive from an ntonio to Houston. bout how far will the have to drive? 17. ustif athematical rguments (1)(G) wo polgons have corresponding side lengths that are proportional. an ou conclude that the polgons are similar? ustif our reasoning. 1. onnect athematical Ideas (1)() plain wh two congruent figures must also be similar. Include scale factor in our eplanation. 1. L and are similar. he scale factor of L to is : 1. What is the scale factor of to L? H In rectangle G, : = 2 :. In rectangle LW, L : = 2 :. how that G LW. G el io cale 1 cm : 112 km ustin Laredo Houston an ntonio Galveston orpus hristi rownsville 4 Lesson -1 imilar olgons

4 21. nalze athematical elationships (1)() compan produces a standard-sized U.. flag that is ft b 5 ft. he compan also produces a giant-sized flag that is similar to the standard-sized flag. If the shorter side of the giant-sized flag is 6 ft, what is the length of its longer side? 22. a. plain athematical Ideas (1)(G) What are the measures of,,,,,, and G? plain. b. What are the lengths of,,,,,, G, and G? c. Is similar to G? ustif our answer. reate epresentations to ommunicate athematical Ideas (1)() hoose a scale and make a scale drawing of each rectangular plaing surface. 2. soccer field is 110 d b 60 d. 24. football field is 60 ft b 160 ft. ind the value of. Give the scale factor of the polgons. 25. WL V 26. G V 6 W G V 4 2 L G O V 27. ppl athematics (1)() he scale drawing at the right is part of a floor plan for a home. he scale is 1 cm = 10 ft. What are the actual dimensions of the famil room? 2. he lengths of the sides of a triangle are in the etended ratio 2 : : 4. he perimeter of the triangle is 54 in. a. he length of the shortest side of a similar triangle is 16 in. What are the lengths of the other two sides of this triangle? b. ompare the ratio of the perimeters of the two triangles to their scale factor. What do ou notice? ining itchen amil room aster bedroom X est ractice 2. L with a scale factor of 4 :. = cm. What is the value of L?. 6 cm. cm cm. 24 cm 0. In the diagram at the right, what is m 1?. 45 G. 75 H Which of the following is O a propert of an isosceles trapezoid?. he base angles are congruent.. he diagonals are perpendicular.. he legs are congruent.. he diagonals are congruent earsonx.com 5

5 4. Given: 5. Given: = 2, 6. Given: #, #, roof roof roof rove: = 2 = V rove: rove: V is isosceles. V plain wh the triangles are similar. hen find the distance represented b ft 0 ft 15 ft 5 ft 6 in. 4 ft 10 ft irror. nalze athematical elationships (1)() t a certain time of da, a 1.-m-tall person standing net to the Washington onument casts a 0.7-m shadow. t the same time, the Washington onument casts a 65.-m shadow. How tall is the Washington onument? 10. a. re two isosceles triangles alwas similar? plain. b. re two right isosceles triangles alwas similar? plain. 11. ppl athematics (1)() 2-ft vertical post casts a 16-in. shadow at the same time that a nearb cell phone tower casts a 120-ft shadow. How tall is the cell phone tower? 12. ustif athematical rguments (1)(G) oes an line that intersects two sides of a triangle and is parallel to the third side of the triangle form two similar triangles? ustif our reasoning. 1. raw an with m = 0. Use a straightedge and compass to construct L so that L. 14. plain athematical Ideas (1)(G) In the diagram at the right, W. and are altitudes. he scale factor of to W is 4 :. What is the ratio of to? plain how ou know. W. has vertices (0, 0), (2, 4), and (4, 2). has vertices roof (0, ), (-1, 5), and (-2, 4). rove that. 6 Lesson - roving riangles imilar

6 or each pair of similar triangles, find the value of Write a proof of the following: n two nonvertical parallel roof lines have equal slopes. Given: onvertical lines / 1 and / 2, / 1 } / 2, and are # to the -ais rove: O = 20. Use the diagram in ercise 1. rove: n two nonvertical lines with equal roof slopes are parallel. 21. Write a paragraph proof to prove the ide-ngle-ide roof imilarit heorem (heorem -1). Given: =, rove: 22. Write a paragraph proof to prove the ide-ide-ide roof imilarit heorem (heorem -2). Given: = = rove: 1 2 X est ractice 2. omplete the statement?. which postulate or theorem are the triangles similar?. ;. ; 2. ;. ; and 2 are alternate interior angles formed b two parallel lines and a transversal. If m 2 = 6, what is m 1?. 22 G. 6 H he length of a rectangle is twice its width. If the perimeter of the rectangle is 72 in., what is the length of the rectangle?. 12 in.. 1 in.. 24 in.. 6 in. 26. Graph (2, 4), (4, 6), (6, 4), and (4, 2). What tpe of polgon is? ustif our answer. earsonx.com 7

7 OLI H O W O I and LIIO XI can page for a Virtual erd tutorial video. Write a similarit statement relating the three triangles in each diagram. or additional support when completing our homework, go to earsonx.com. 1. L 2.. O ind the geometric mean of each pair of numbers and and and 125 elect echniques to olve roblems (1)() olve for and nalze athematical elationships (1)() he architect s side view drawing of a saltbo-stle house shows a post that supports the roof ridge. he support post is 10 ft tall. How far from the front of the house is the support post positioned? 12. a. he altitude to the hpotenuse of a right triangle divides the hpotenuse into segments 2 cm and cm long. ind the length of the altitude to the hpotenuse. b. Use a ruler to make an accurate drawing of the right triangle in part (a). c. escribe how ou drew the triangle in part (b). ind the geometric mean of each pair of numbers and and and and and 17 ront edroom Living room 25 ft upport post itchen ack 1. valuate easonableness (1)() classmate sas the following statement is true: he geometric mean of positive numbers a and b is 1ab. o ou agree? plain. 1. Write all possible similarit statements relating pairs of triangles in the diagram at the right. 20. Use a roblem-olving odel (1)() he altitude to the hpotenuse of a right triangle divides the hpotenuse into segments with lengths in the ratio 1 : 2. he length of the altitude is. How long is the hpotenuse? earsonx.com 40

8 olve for rove the orollar to the riangle roportionalit heorem. In the diagram from page 40, draw the auiliar line < W > roof and label its intersection with line b as point. Given: a } b } c rove: = WX XY a b c X W Y 1. ustif athematical rguments (1)(G) Use the definition in part (a) roof to prove the statements in parts (b) and (c). a. Write a definition for a midsegment of a parallelogram. b. parallelogram midsegment is parallel to two sides of the parallelogram. c. parallelogram midsegment bisects the diagonals of a parallelogram. 20. rove the riangle-ngle-isector heorem. In the diagram at the top of page 40, draw the auiliar line < > so that < > roof }. tend to meet < > at point. Given: < > bisects. rove: = ppl athematics (1)() In Washington,..,. apitol treet, Independence venue, treet, and treet are parallel streets that intersect entuck venue and 12th treet. 21. How long (to the nearest foot) is entuck venue between treet and treet? 22. How long (to the nearest foot) is entuck venue between. apitol treet and Independence venue? 2. n angle bisector of a triangle divides the opposite side of the triangle into segments 5 cm and cm long. second side of the triangle is 7.5 cm long. ind all possible lengths for the third side of the triangle. Lincoln ark 600 ft 00 ft 12th t. apitol t. Independence ve. 460 ft Walter t. t. outh arolina ve. t. entuck ve ft 1th t. assachusetts ve. t. 14th t. earsonx.com 41