1 2-5 proving angles congruent objectives: identify relationships between angles that are:...

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2-5 Proving Angles Congruent

Objectives:

• Identify relationships between angles that are:– Vertical– Complementary– Supplementary

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Recall: Angle Pairs – Vertical Angles

• Vertical Angles

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Vertical angles:

1 and 3

2 and 4

Angles

Vertical

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Conjecture about Vertical Angles

1) On a sheet of paper, construct two intersecting lines that are not perpendicular.

2) With a protractor, measure each of the four angles formed.

3) Make a conjecture about vertical angles.

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Vertical Angles Theorem

Vertical angles are congruent.

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1 and 3 are congruent

2 and 4 are congruent

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Congruent Complements Theorem

If two angles are congruent, then their complements are_________.

The measure of angles complementary to A and Bis 30.

A B60° 60°

A B

congruent

Recall:

• Complementary Angles can be formed by

Corner (90 degrees)

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Congruent Supplements Theorem• Recall:

• Supplementary Angles can be formed by

Straight Lines (180 degrees)

If two angles are congruent, then their supplements are_________.

The measure of angles supplementary to 1 and 4is 110.

70° 70°4 3 2 1

110° 110°

4 1

congruent