Download Right Angles Congruence Theorem

Geometry 2.7
Big Idea: Prove
Angle Pair
Relationships
Theorem 2.3:
Right Angles Congruence
Theorem
All right angles are
congruent.
Theorem 2.4:
Congruent Supplements
Theorem
If two angles are
supplementary to the
same angle (or to
congruent angles),then
they are congruent.
Example
If angles 1 and 3 are supplementary and
angles 5 and 3 are supplementary, then
angles 1 and 5 are congruent.
Theorem 2.5:
Congruent Complements
Theorem
If two angles are
complementary to the
same angle (or to
congruent angles),then
they are congruent.
Example
1
2
3
If angles 1 and 2 are complementary
and angles 1 and 3 are
complementary, then angles 2 and 3
are congruent.
Theorem 2.6:
Vertical Angles Congruence
Theorem
Vertical angles are
congruent.
Example
4
1
2
3
Postulate 12:
Linear Pair Postulate
If two angles form a linear
pair, then they are
supplementary.
Example
Since angles 1 and 2 form a linear
pair, they must be supplementary
and m 1 + m 2 = 180º
Proof 1: Right Angles Congruence
Theorem
Given: PQR and UTS are right angles
Prove: PQR
UTS
Given: PQR and UTS are right angles
Prove: PQR
UTS
Statement
Reason
1.
1.
2. m PQR = 90º; 2.
m UTS = 90º
3.m PQR = m UTS 3.
4.
4.
5.
5.
Example
If m 1 = 112º, find the measure
of angles 2, 3 & 4.