CCGPS Geometry
Unit 1- Similarity, Congruence & Proofs
1 – Notes
Complementary and Supplementary Angles
TYPES OF ANGLES:
1. Acute: Acute angles have measures between 0° and 90°.
2. Right: A right angle has measure equal to 90°.
3. Obtuse: Obtuse angles have measures between 90° and 180°.
Sketch:
SPECIAL PAIRS OF ANGLES:
1. Complementary Angles: Pair of angles whose sum of measures equals 90°.
2. Supplementary Angles: Pair of angles whose sum of measures equals 180°.
3. Angle Bisector: A ray (or line or segment) that divides an angle into two
congruent angles (two angles with equal measure).
Vertical Angles & Linear Pair
If two angles share a vertex and together they make a straight angle, then the two
angles are called a linear pair.
Linear pairs could be defined as being supplementary angles because they always add
up to 180º. Are all supplementary angles linear pairs? Why?
Two angles are vertical angles if their sides form two pairs of opposite rays and they
share a common vertex. Why? How do you prove that they are congruent?
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CCGPS Geometry
Unit 1- Similarity, Congruence & Proofs
1 – Notes
Practice:
1. Can two supplementary angles both be obtuse angles? Acute angles? Why?
2. Can two supplementary angles both be right angles? Why?
3. Refer to the diagram to answer each. BE is an angle bisector.
a) If mABE = 40, find mEBC.
b) If mABC = 70, find mABE.
4. 1 and 2 are complementary. Solve for x and the measure of both angles.
1  5 x  2
2  2 x  4
5. One of two complementary angles is 36° greater than its complement. Find the
measure of both angles.
6.
One of two supplementary angles is 123° less than twice its supplement. Find the
measure of both angles.
Practice Problems: Solve for the missing variable(s).
1)
2)
xᵒ
130 yᵒ
ᵒ zᵒ
3)
(2x – 17)ᵒ
122
ᵒ
(x – 12)ᵒ
105
ᵒ
(2x + 5)ᵒ
4)
(x + 55)ᵒ
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