See Problem 2.

What other information, if any, do you need to prove the two triangles congruent by SAS? Explain.

See Problem 3.

Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SAS, write not enough information. Explain your answer.

B Apply

15. Think About a Plan You and a friend are cutting triangles out of felt for an art project. You want all the triangles to be congruent. Your friend tells you that each triangle should have two 5-in. sides and a 40 ° 40 degrees  angle. If you follow this rule, will all your felt triangles be congruent? Explain.
    • How can you use diagrams to help you?
    • Which postulate, SSS or SAS, are you likely to apply to the given situation?
16. Proof Given: B C ¯ ≅ D A ¯ , ∠ C B D ≅ ∠ A D B b c bar , approximately equal to . d eh bar , comma . angle c b d approximately equal to . angle eh d b

    Prove: Δ B C D ≅ Δ D A B cap delta b c d approximately equal to cap delta d eh b

    

17. Proof Given: X is the midpoint of A G ¯ eh g bar  and N R ¯ . n r bar , .

    Prove: Δ A N X ≅ Δ G R X cap delta eh n x approximately equal to cap delta g r x

    

Use the Distance Formula to determine whether Δ A B C cap delta eh b c  and Δ D E F cap delta d e f  are congruent. Justify your answer.

18. A ( 1 , 4 ) , B ( 5 , 5 ) , C ( 2 , 2 ) ; eh open 1 comma 4 close comma b open 5 comma 5 close comma c open 2 comma 2 close semicolon

    D ( − 5 , 1 ) , E ( − 1 , 0 ) , F ( − 4 , 3 ) d open negative 5 comma 1 close comma e open negative 1 comma 0 close comma f open negative 4 comma 3 close

19. A ( 3 , 8 ) , B ( 8 , 12 ) , C ( 10 , 5 ) ; eh open 3 comma 8 close comma b open 8 comma 12 close comma c open 10 comma 5 close semicolon

    D ( 3 , − 1 ) , E ( 7 , − 7 ) , F ( 12 , − 2 ) d open 3 comma negative 1 close comma e open 7 comma negative 7 close comma f open 12 comma negative 2 close

20. A ( 2 , 9 ) , B ( 2 , 4 ) , C ( 5 , 4 ) ; eh open 2 comma 9 close comma b open 2 comma 4 close comma c open 5 comma 4 close semicolon

    D ( 1 , − 3 ) , E ( 1 , 2 ) , F ( − 2 , 2 ) d open 1 comma negative 3 close comma e open 1 comma 2 close comma f open negative 2 comma 2 close

21. Writing List three real-life uses of congruent triangles. For each real-life use, describe why you think congruence is necessary.

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