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EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2? SOLUTION AB and BC are perpendicular, so by Theorem 3.9, they form four right angles. You can conclude that 1 and 2 are right angles, so 1 2.

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GUIDED PRACTICE for Examples 1 and 2 Given that ABC  ABD, what can you conclude about 3 and 4 ? Explain how you know. 1. They are complementary. Sample Answer: ABD is a right angle since 2 lines intersect to form a linear pair of congruent angles (Theorem 3.8 ), 3 and 4 are complementary. ANSWER

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Page 1: EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2 ? SOLUTION AB…

EXAMPLE 1 Draw Conclusions

In the diagram, AB BC. What can you conclude about 1 and 2?

SOLUTION

AB and BC are perpendicular, so by Theorem 3.9, they form four right angles. You can conclude that 1 and 2 are right angles, so 1 2.

Page 2: EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2 ? SOLUTION AB…

EXAMPLE 2 Prove Theorem 3.10

Prove that if two sides of two adjacentacute angles are perpendicular, then theangles are complementary.

Given ED EF

Prove 7 and 8 are complementary.

Page 3: EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2 ? SOLUTION AB…

GUIDED PRACTICE for Examples 1 and 2

Given that ABC ABD, what can you conclude about 3 and 4? Explain how you know.

1.

They are complementary.Sample Answer: ABD is a right angle since 2 linesintersect to form a linear pair of congruent angles (Theorem 3.8), 3 and 4 are complementary.

ANSWER


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