Download Identifying Vertical Angles and Linear Pairs

BELLWORK
3) Solve for y. Given: AC=21. State the
reason that justifies each step.
2y
A
1)
2)
3)
4)
5)
AB + BC = AC
2y + (3y-9) = 21
5y - 9 = 21
5y = 30
y= 6
3y-9
B
C
1)
2)
3)
4)
5)
Segment addition postulate
Substitution property
Simplify
Addition property of equality
Division property of equality
2-5 Proving Angles Congruent
Geometry
Adjacent Angles
Adjacent angles- two coplanar angles with a
common side, a common vertex, and no
common interior points.
5 6
Vertical Angles and Linear Pairs
Two angles are vertical angles if
their sides form two pairs of
opposite rays.
Two adjacent angles are a linear
pair if their noncommon sides
are opposite rays.
1
2
4
3
1 and 3 are vertical angles.
2 and 4 are vertical angles.
5
6
5 and 6 are a linear pair.
Complementary and Supplementary Angles
Complementary angles – Two angles whose
sum is 90˚.
*Complementary angles can be adjacent or
nonadjacent.
4
1
2
complementary
adjacent
3
complementary
nonadjacent
Complementary and Supplementary Angles
Supplementary angles- Two Angles whose measures
have a sum of 180.
* Supplementary angles can be adjacent or non adjacent
5 6
supplementary
adjacent
7
8
supplementary
nonadjacent
Identifying Vertical Angles and Linear Pairs
Answer the questions using the diagram.
Are 2 and 3 a linear pair?
1
2
4
3
SOLUTION
No. The angles are adjacent but their noncommon sides are not opposite rays.
Identifying Vertical Angles and Linear Pairs
Answer the questions using the diagram.
Are 2 and 3 a linear pair?
Are 3 and 4 a linear pair? Supplementary?
1
2
4
3
SOLUTION
No. The angles are adjacent but their noncommon sides are not opposite rays.
Yes. The angles are adjacent and their noncommon sides are opposite rays.
Identifying Vertical Angles and Linear Pairs
Answer the questions using the diagram.
Are 2 and 3 a linear pair?
Are 3 and 4 a linear pair?
Are 1 and 3 vertical angles?
1
2
4
3
SOLUTION
No. The angles are adjacent but their noncommon sides are not opposite rays.
Yes. The angles are adjacent and their noncommon sides are opposite rays.
No. The sides of the angles do not form two pairs of opposite rays.
Identifying Vertical Angles and Linear Pairs
Answer the questions using the diagram.
Are 2 and 3 a linear pair?
Are 3 and 4 a linear pair?
Are 1 and 3 vertical angles?
Are 2 and 4 vertical angles?
1
2
4
3
SOLUTION
No. The angles are adjacent but their noncommon sides are not opposite rays.
Yes. The angles are adjacent and their noncommon sides are opposite rays.
No. The sides of the angles do not form two pairs of opposite rays.
No. The sides of the angles do not form two pairs of opposite rays.
Congruent Supplements
Theorem
•
Theorem 2-2: Congruent Supplements.
If two angles are supplementary to the
same angle (or to congruent angles), then
they are congruent.
Congruent Complements
Theorem
•
•
•
Theorem 2-3: If two angles are
complementary to the same angle (or
congruent angles), then the two angles
are congruent.
Theorem 2-4: All right angles are
congruent
Theorem 2-5: If two angles are congruent
and supplementary, then each is a right
angle