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Section 2-8
Pages 124-131
Proving Angle Relationships
After today’s lesson you should be able to:
- Write proofs involving supplementary and complementary
angles.
- Write proofs involving congruent and right angles.
Review: Supplementary angles add up to 180.
Complementary angles add up to 90.
Congruent angles have the same measure.
Vertical angles are congruent.
New Postulates and Theorems:
Postulate 2.10 (Protractor Postulate) Given ray AB and a number r
between 0 and 180, there is exactly one ray with endpoint A,
extending on either side of ray AB, such that the measure of
the angle formed is r.
Postulate 2.11 (Angle Addition) If R is in the interior of LPQS, then
mLPQR + mLRQS = mLPQS.
If mLPQR + mLRQS = mLPQS, then R is in the interior of
LPQS.
Theorem 2.3 (Supplement Theorem) If two angles form a linear pair,
then they are supplementary angles.
Theorem 2.4 (Complement Theorem) If the noncommon sides of
two adjacent angles form a right angle, then the angles are
complementary angles.
Theorem 2.5: Congruence of angles is reflexive, symmetric, and
transitive.
Theorem 2.6: Angles supplementary to the same angle or to
congruent angles are congruent.
(L’s suppl. to same L or  L’s are )
Theorem 2.7: Angles complementary to the same angle or to
congruent angles are congruent.
(L’s compl. to same L or  L’s are )
Theorem 2.8 (Vertical Angles Theorem) If two angles are vertical
angles, then they are congruent.
Theorem 2.9: Perpendicular lines intersect to form four right angles.
Theorem 2.10: All right angles are congruent.
Theorem 2.11: Perpendicular lines form congruent adjacent angles.
Theorem 2.12: If two angles are congruent and supplementary, then
each angle is a right angle.
Theorem 2.13: If two congruent angles form a linear pair, then they
are right angles.
Ex. 1: L6 and L8 are complementary, L8 = 47.
6
Ex. 2:
7
8
m(11) = x – 4, m(12) = 2x – 5.
11
12
W
Ex. 3:
Given: VX bisects LWVY
VY bisects LXVZ
Prove: LWVX  LYVZ
V
X
Z
Statements
Reasons
Y