2-5 Proving Angles Congruent

1
2-5 Proving Angles Congruent

• Objectives
• Identify relationships between angles that are
• Vertical
• Complementary
• Supplementary

2
Recall Angle Pairs Vertical Angles

• Vertical Angles

Vertical angles
?1 and ?3
1
4
2
?2 and ?4
3
Vertical
Angles
3
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.
1
4
2
3
4
Vertical Angles Theorem

• Vertical angles are congruent.

?1 and ?3 are congruent
1
4
2
3
?2 and ?4 are congruent
5
Congruent Complements Theorem

• Recall
• Complementary Angles can be formed by
• Corner (90 degrees)

If two angles are congruent, then their
complements are _________.
congruent
?A ? ?B
The measure of angles complementary to ?A and
?B is 30.
6
Congruent Supplements Theorem

• Recall
• Supplementary Angles can be formed by
• Straight Lines (180 degrees)

If two angles are congruent, then their
supplements are _________.
congruent
The measure of angles supplementary to ?1 and
?4 is 110.
110
70
70
110
?4 ? ?1