15. Think About a Plan Δ A B C cap delta eh b c  and Δ P Q R cap delta p q r  are right triangular sections of a fire escape, as shown. Is each story of the building the same height? Explain.

    

    • What can you tell from the diagram?
    • How can you use congruent triangles here?
16. Writing “A HA!” exclaims your classmate. “There must be an HA Theorem, sort of like the HL Theorem!” Is your classmate correct? Explain.
17. Proof Given: R S ¯ ≅ T U ¯ , R S ¯ ⊥ S T ¯ , T U ¯ ⊥ U V ¯ , T r s bar , approximately equal to . t u bar , comma . r s bar , up tack . s t bar , comma . t u bar , up tack , u v bar , comma t  is the midpoint of R V ¯ r v bar

    Prove: Δ R S T ≅ Δ T U V cap delta r s t approximately equal to cap delta t u v

    

18. Proof Given: Δ L N P cap delta l n p  is isosceles with base N P ¯ , M N ¯ ⊥ N L ¯ , Q P ¯ ⊥ P L ¯ , M L ¯ ≅ Q L ¯ n p bar , comma . m n bar , up tack . n l bar , comma . q p bar , up tack . p l bar , comma . m l bar , approximately equal to . q l bar

    Prove: Δ M N L ≅ Δ Q P L cap delta m n l approximately equal to cap delta q p l

    

Constructions Copy the triangle and construct a triangle congruent to it using the given method.

19. SAS
20. HL
21. ASA
22. SSS

    

23. Proof Given: Δ G K E cap delta g k e  is isosceles with base G E ¯ , ∠ L g e bar , comma . angle l  and ∠ D angle cap d  are right angles, and K is the midpoint of L D ¯ . l d bar , .

    Prove: L G ¯ ≅ D E ¯ l g bar , approximately equal to . d e bar

    

24. Proof Given: L O ¯ l o bar  bisects ∠ M L N , O M ¯ ⊥ L M ¯ , O N ¯ ⊥ L N ¯ angle m l n comma . o m bar , up tack . l m bar , comma . o n bar , up tack , l n bar

    Prove: Δ L M O ≅ Δ L N O cap delta l m o approximately equal to cap delta l n o

    

25. Reasoning Are the triangles congruent? Explain.

    

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