Practice and Problem-Solving Exercises

A Practice

See Problem 1.

8. Construction Builders use the king post truss (below left) for the top of a simple structure. In this truss, Δ A B C ≅ Δ A B D . cap delta eh b c approximately equal to cap delta eh b d .  List the congruent corresponding parts.

   

9. The attic frame truss (above right) provides open space in the center for storage. In this truss, Δ E F G ≅ Δ H I J . cap delta e f g approximately equal to cap delta h i j .  List the congruent corresponding parts.

Δ L M C ≅ Δ B J K . cap delta l m c approximately equal to cap delta b j k .  Complete the congruence statements.

10. L C ¯ ≅ l c bar , approximately equal to  __?__
11. K J ¯ ≅ k j bar , approximately equal to  __?__
12. J B ¯ ≅ j b bar , approximately equal to  __?__
13. ∠ L ≅ angle l approximately equal to  __?__
14. ∠ K ≅ angle k approximately equal to  __?__
15. ∠ M ≅ angle m approximately equal to  __?__
16. Δ C M L ≅ cap delta c m l approximately equal to  __?__
17. Δ K B J ≅ cap delta k b j approximately equal to  __?__
18. Δ M L C ≅ cap delta m l c approximately equal to  __?__
19. Δ J K B ≅ cap delta j k b approximately equal to  __?__

P O L Y ≅ S I D E . p o l y approximately equal to s i d e .  List each of the following.

20. four pairs of congruent sides
21. four pairs of congruent angles

See Problem 2.

At an archeological site, the remains of two ancient step pyramids are congruent. If A B C D ≅ E F G H , eh b c d approximately equal to e f g h comma  find each of the following. (Diagrams are not to scale.)

Image Long Description

22. AD
23. GH
24. m ∠ G H E m angle g h e
25. m ∠ B A D m angle b eh d
26. EF
27. BC
28. m ∠ D C B m angle d c b
29. m ∠ E F G m angle e f g

See Problem 3.

For Exercises 30 and 31, can you conclude that the triangles are congruent? Justify your answers.

30. Δ T R K cap delta t r k  and Δ T U K cap delta t u k

    

31. Δ S P Q cap delta s p q  and Δ T U V cap delta t u v

    

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