4-1. Standardized Test Prep. Multiple Choice. Short Response. Congruent Figures. For Exercises 1 6, choose the correct letter.

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1 Name lass ate - tandardized est rep ongruent igures ultiple hoice or xercises, choose the correct letter.. he pair of polygons at the right is congruent. What is m/?. he triangles at the right are congruent. Which of the following statements must be true? / > / > / > / >. iven the diagram at the right, which of the following must be true? nx > nx nx > nx nx > nx nx > nx X. f n > nxyz, which of the following need not be true? / > /X / > /Z > XZ > YZ. f n > n, m/, and m/, what is m/?. f >, m/ x, and m/ x, what is m/? [] l Ol and l Ol, both by the lt. nt ngles hm. o, by hird ngles hm., l Ol. ecause O by the efl. rop. of ongruence, and we know O and O, then all the corresponding parts are congruent and k Ok. [] incomplete proof [] no proof or incorrect proof hort esponse. iven:,, >, > rove: n > n rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved.

2 Name lass ate - tandardized est rep riangle ongruence by and ultiple hoice or xercises, choose the correct letter.. Which pair of triangles can be proved congruent by?. Which pair of triangles can be proved congruent by?. What additional information do you need to prove nno > n? N > / > / NO > /O > / N O. What additional information do you need to prove n > n? > / > / > > hort esponse. Write a two-column proof. L iven: is the midpoint of L, >. rove: nl > n [] tatements: ) is the midpoint of L; ) L O ; ) ll Ol; ) O ; ) kl Ok; easons: ) iven; ) ef. of a midpoint; ) Vert. ' are O; ) iven; ) [] incomplete proof [] incorrect or no proof rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved.

3 Name lass ate - tandardized est rep riangle ongruence by and ultiple hoice or xercises, choose the correct letter.. Which pair of triangles can be proven congruent by the ostulate? L U N V W K X Y Z L. or the ostulate to apply, which side of the triangle must be known? the included side the shortest side the longest side a non-included side. Which pair of triangles can be proven congruent by the heorem? K L O K. or the heorem to apply, which side of the triangle must be known? the included side the longest side hort esponse. Write a paragraph proof. iven: / > /, / > / rove: nvwx > nvyx W V Y the shortest side a non-included side [] l Ol is given. l Ol because vert. ' are O. l Ol by the rans. rop. of O. l Ol X is given. VX O VX by the efl. rop. of O. kvwx OkVYX by. [] incomplete proof [] incorrect or no proof rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved.

4 Name lass ate - tandardized est rep Using orresponding arts of ongruent riangles ultiple hoice or xercises, choose the correct letter.. ased on the given information in the figure at the right, how can you justify that n > n?. n the figure at the right the following is true: / > / and / > /. ow can you justify that n > n?. n > nkyz. ow can you justify that YZ >?. Which statement cannot be justified given only that n > n? > / > / / > / >. n the figure at the right, which theorem or postulate can you use to prove n > nz?. n the figure at the right, which theorem or postulate can you use to prove nk > n? Z K hort esponse. What would a brief plan for the following proof look like? iven: >, / > / rove: > [] O by the eflexive roperty. k Ok by. O by ; [] one step missing or one reason incorrect [] incorrect or no response rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved.

5 rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved. Name lass ate - tandardized est rep sosceles and quilateral riangles ridded esponse olve each exercise and enter your answer on the grid provided. efer to the diagram for xercises.. What is the value of x?. What is the value of y?. What is the value of z?. he measures of two of the sides of an equilateral triangle are x in. and x in. What is the measure of the third side in inches?. n n,, m/ x, and m/ x. What is m/? y x z nswers.....

6 Name lass ate - tandardized est rep ongruence in ight riangles ultiple hoice or xercises, choose the correct letter.. Which additional piece of information would allow you to prove that the triangles are congruent by the L theorem? m/ m/ m/ > >. or what values of x and y are the triangles shown congruent? x, y x, y x, y x, y x x y x x y. wo triangles have two pairs of corresponding sides that are congruent. What else must be true for the triangles to be congruent by the L heorem? he included angles must be right angles. hey have one pair of congruent angles. oth triangles must be isosceles. here are right angles adjacent to just one pair of congruent sides.. Which of the following statements is true? n > n by. n > n by. n > n by L. n > n by L. xtended esponse. re the given triangles congruent by the L heorem? xplain. [] No; they are right triangles, and have a pair of congruent legs ( O ), but the hypotenuses, and, are not congruent. o, the triangles only meet two of the three conditions for congruence by the L heorem. [] appropriate response plus a discussion of two of the three criteria for congruence [] recognition only that the hypotenuses are not congruent [] recognition that the triangles are not congruent [] incorrect or no response rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved.

7 Name lass ate - tandardized est rep ongruence in Overlapping riangles ultiple hoice or xercises, choose the correct letter.. What is the common angle of n and n? / / / /U U Use the following information for xercises. iven: nzwx > nyxw, ZW YX Z Y rove: nzw > nyx W X. Which corresponding parts statement is needed to prove nzw > nyx? /ZW > /YX ZW YX /Z > / WX WX. classmate writes the statement /ZW > /YX to help prove the congruence of the triangles. What reason should the classmate give? iven ngles cut by a bisector are congruent. ase angles of an isosceles triangle are congruent. Vertical angles are congruent.. fter using the congruence statements from xercises and, which statement can be used to prove the triangles congruent? /Z > /Y WX > WX /ZW > /YX W > X. Which theorem or postulate will prove nzw > nyx? hort esponse. n the diagram at the right, which two triangles should be proved congruent first to help prove n > n? [] k and k [] orrect > named but vertices do not correspond. [] incorrect > named rentice all eometry eaching esources opyright by earson ducation, nc., or its affiliates. ll ights eserved.