Notes Section 2.8
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Transcript 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 m2 = 67, find
m1.
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 m2 = 72, find m1.
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