Geometry Notes
Sections 2-8
What you’ll learn
How to write proofs involving supplementary and complementary angles
How to write proofs involving congruent and right angles
Vocabulary There is no new vocabulary However. . . Do you know these definitions. . .?
Supplementary AnglesComplementary AnglesReflexive PropertySymmetric PropertyTransitive PropertyPerpendicular linesLinear Pair of AnglesVertical AnglesCongruent Angles
Adjacent AnglesCongruent Segments Angle Addition PostulateSegment Addition PostulateMidpointSegment BisectorAngle BisectorOpposite Rays I hope so. . . .
Congruence of Segments is . . .
Reflexive segments
Symmetric segments
Transitive segments
A segment is congruent to itself.
AB AB
You can switch the left and right sides
If AB CD then CD AB.
If AB CD and CD EF, then AB EF.
Congruence of Angles is . . .
Reflexive angles
Symmetric angles
Transitive angles
An angle is congruent to itself.
A A
You can switch the left and right sides
If A B then B A.
If A B and B C, then A C.
Supplement Theorem
What are we given?Look in the hypothesis of the conditional statement and draw it.
Now what can we conclude?Look in the conclusion of the conditional statement 1 and 2 are supplementary.
If two angles form a linear pair,
then they are supplementary.
two angles form a linear pair, 1
2
they are supplementary
How does this work in problems?
Linear pairs → supplementary → add up to 180
12
If 1 and 2 form a linear pair and m2 = 67, find m1.
More example problems
Linear pairs → supplementary → add up to 180
Find the measure of each angle.
More example problems
Linear pairs → supplementary → add up to 180
Find the measure of each angle.
Vertical Angles We’ve done this before.
Draw two vertical angles If two angles are vertical angles then they
are congruent.
Vert. s → → =
How does this work in problems?
1 2
If m2 = 72, find m1.
Vert. s → → =
More example problems
Find the measure of each angle.
Vert. s → → =
More theorems. . . Complement theorem If the noncommon sides of two adjacent angles
form a right angle, then the angles are complementary angles.
1
2
1 & 2 complementary → m 1 + m 2 = 90
More theorems. . . Angles supplementary to the same angle
or to two congruent angles are congruent.
More theorems. . . Angles complementary to the same angle
or to two congruent angles are congruent.
More theorems. . . Perpendicular lines intersect to form four
right angles. All right angles are congruent. Perpendicular lines form congruent
adjacent angles. If two angles are congruent and
supplementary, then each angle is a right angle.
If two congruent angles form a linear pair, then they are right angles.
Have you learned .. . .
How to write proofs involving supplementary and complementary angles?
How to write proofs involving congruent and right angles?
Assignment: Worksheet 2.8A