3) Solve for y. Given: AC=21. State the reason that justifies each step.

1) AB + BC = AC

2) 2y + (3y-9) = 21

3) 5y - 9 = 21

4) 5y = 30

5) y= 6

1) Segment addition postulate

2) Substitution property

3) Simplify

4) Addition property of equality

5) Division property of equality

2y 3y-9

A B C

BELLWORK

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

1 and 3 are vertical angles.

2 and 4 are vertical angles.

5 and 6 are a linear pair.

14

3

25 6

Two adjacent angles are a linear pair if their noncommon sides are opposite rays.

Two angles are vertical angles if their sides form two pairs of opposite rays.

Complementary and Supplementary Angles

Complementary angles – Two angles whose sum is 90˚. *Complementary angles can be adjacent or nonadjacent.

12 3

4

complementary adjacent

complementary nonadjacent

Complementary and Supplementary Angles

5 67 8

supplementary nonadjacent

supplementary adjacent

Supplementary angles- Two Angles whose measures have a sum of 180.* Supplementary angles can be adjacent or non adjacent

Identifying Vertical Angles and Linear Pairs

Answer the questions using the diagram.

1 2

4 3

Are 2 and 3 a linear pair?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.No.

Identifying Vertical Angles and Linear Pairs

Answer the questions using the diagram.

1 2

4 3

Are 2 and 3 a linear pair?

Are 3 and 4 a linear pair? Supplementary?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

The angles are adjacent and their noncommon sides are opposite rays.

No.

Yes.

Identifying Vertical Angles and Linear Pairs

Answer the questions using the diagram.

1 2

4 3

Are 2 and 3 a linear pair?

Are 3 and 4 a linear pair?

Are 1 and 3 vertical angles?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

The angles are adjacent and their noncommon sides are opposite rays.

The sides of the angles do not form two pairs of opposite rays.

No.

Yes.

No.

Identifying Vertical Angles and Linear Pairs

Answer the questions using the diagram.

1 2

4 3

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?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

The angles are adjacent and their noncommon sides are opposite rays.

The sides of the angles do not form two pairs of opposite rays.

The sides of the angles do not form two pairs of opposite rays.

No.

Yes.

No.

No.

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