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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.
12
34
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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