Download Notes Section 2.8

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 Angles  Adjacent Angles
 Complementary Angles  Congruent Segments
 Reflexive Property
 Angle Addition Postulate
 Symmetric Property
 Segment Addition Postulate
 Transitive Property
 Midpoint
 Perpendicular lines
 Segment Bisector
 Linear Pair of Angles
 Angle Bisector
 Vertical Angles
 Opposite Rays
 Congruent Angles
 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
An angle is congruent to itself.
A  A
You can switch the left and right sides
Symmetric
 angles
If A  B then B  A.
Transitive
 angles
If A  B and B  C, then
A  C.
Supplement Theorem
 If


two angles form a linear pair,
2
1
then they are supplementary
supplementary.
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.
How does this work in problems?
If 1 and 2 form a linear
pair and m2 = 67, find
m1.

1
2
Linear pairs → supplementary → add up to 180
More example problems
Find the measure of each angle.

Linear pairs → supplementary → add up to 180
More example problems
Find the measure of each angle.

Linear pairs → supplementary → add up to 180
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?
If m2 = 72, find m1.

Vert. s →  → =
1
2
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.
2
1
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