28. Proof Identify a pair of overlapping congruent triangles in the diagram. Then use the given information to write a proof to show that the triangles are congruent.

    Given: A C ¯ ≅ B C ¯ , ∠ A ≅ ∠ B eh c bar , approximately equal to . b c bar , comma . angle eh approximately equal to angle b

    

Standardized Test Prep

SAT/ACT

29. According to the diagram below, which statement is true?

    

    1. Δ D E H ≅ Δ G F H cap delta d e h approximately equal to cap delta g f h  by AAS
    2. Δ D E H ≅ Δ G F H cap delta d e h approximately equal to cap delta g f h  by SAS
    3. Δ D E F ≅ Δ G F E cap delta d e f approximately equal to cap delta g f e  by AAS
    4. Δ D E F ≅ Δ G F E cap delta d e f approximately equal to cap delta g f e  by SAS
30. Δ A B C cap delta eh b c  is isosceles with base A C ¯ . eh c bar , .  If m ∠ C = 37 , m angle . c equals 37 comma  what is m ∠ B ? m angle b question mark
    6. 37
    7. 74
    8. 106
    9. 143
31. Which word correctly completes the statement “All __?__ angles are congruent”?
    1. adjacent
    2. supplementary
    3. right
    4. corresponding
32. Extended Response In the figure, L J ¯ | | G K ¯ l j bar , vertical line vertical line , g k bar  and M is the midpoint of L G ¯ . l g bar , .
    1. Copy the diagram. Then mark your diagram with the given information.
    2. Prove Δ L J M ≅ Δ G K M . cap delta l j m approximately equal to cap delta g k m .

    3. Can you prove that Δ L J M ≅ Δ G K M cap delta l j m approximately equal to cap delta g k m  another way? Explain.

       

Mixed Review

See Lesson 4-6.

33. Developing Proof Complete the paragraph proof.

    Given: A B ¯ ≅ D B ¯ , ∠ A eh b bar , approximately equal to . d b bar , comma . angle eh  and ∠ D angle d  are right angles

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

    Proof: You are given that A B ¯ ≅ D B ¯ eh b bar , approximately equal to . d b bar  and ∠ A angle eh  and ∠ D angle d  are right angles. Δ A B C cap delta eh b c  and Δ D B C cap delta d b c  are a. __?__ triangles by the definition of b. __?__ triangle. B C ¯ ≅ B C ¯ b c bar , approximately equal to . b c bar  by the c. __?__ Property of Congruence. Δ A B C ≅ Δ D B C cap delta eh b c approximately equal to cap delta d b c  by the d. __?__ Theorem.

    

See Lesson 3-6.

34. Constructions Draw a line p and a point M not on p. Then construct line n through M so that n ⊥ p . n up tack p .

Get Ready! To prepare for Lesson 5-1, do Exercises 35−37.

See Lesson 1-7.

Find the coordinates of the midpoint of A B ¯ . eh b bar , .

35. A ( − 2 , 3 ) , B ( 4 , 1 ) eh open negative 2 comma 3 close comma b open 4 comma 1 close
36. A ( 0 , 5 ) , B ( 3 , 6 ) eh open 0 comma 5 close comma b open 3 comma 6 close
37. A ( 7 , 10 ) , B ( − 5 , − 8 ) eh open 7 comma 10 close comma b open negative 5 comma negative 8 close

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