geometry lesson 2 – 8 proving angle relationships objective: write proofs involving supplementary...
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GeometryLesson 2 – 8
Proving Angle Relationships
Objective:Write proofs involving supplementary angles.
Write proofs involving congruent and right angles.
Postulate 2.10
Protractor PostulateGiven any angle, the measure can be put into
one-to-one correspondence with real numbers between 0 and 180.
ExampleIf .3,131231 ofmeasurethefindABCmandmJustify each step.
ABCmmmm 321 Angle Add. Post.
13139023 m Sub
1313113 m Sub
1131311133113 m Subt. Prop.
183 m Sub
Theorems
Supplement Theorem If two angles form a linear pair, then they
are supplementary angles.
Complement Theorem If the noncommon sides of two adjacent
angles form a right angle, then the angles are complementary angles.
Angles 6 & 7 form a linear pair. Example
.7&,6,,1257&3236 mmxfindxmxmIfJustify each step.
18076 mm Supplement Thm.
3x + 32 + 5x + 12 = 180 Sub
8x + 44 = 180 Sub
8x + 44 - 44 = 180 - 44 Subt. Prop.
8x = 136 Sub
8
136
8
8x
Division Prop.
x = 17 Sub977
836
m
m
TheoremCongruent Supplement TheoremAngles supplementary to the same angle
or to congruent angles are congruent.
Abbreviation:
TheoremCongruent Complements TheoremAngles complementary to the same angle
or congruent angles are congruent.
Abbreviation
Right Angle Theorems
Theorem 2.9Perpendicular lines intersect to form 4 right
angles
Theorem 2.10All right angles are congruent.
Theorem 2.11Perpendicular lines from 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.