PARALLEL LINES CUT BY A TRANSVERSAL

DEFINITIONS PARALLEL TRANSVERSAL ANGLE VERTICAL ANGLE CORRESPONDING ANGLE ALTERNATE INTERIOR ANGLE ALTERNATE EXTERIOR ANGLE

DEFINITIONS SUPPLEMENTARY ANGLE COMPLEMENTARY ANGLE CONGRUENT

Some special angles you need to know Linear Pair These angles are adjacent and supplementary. 1 2

One more special angle Vertical angles Vertical angles form two sets of opposite rays. They are always congruent. 4 3

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 1 and < 2 are called SUPLEMENTARY ANGLES They form a straight angle measuring 180 degrees.

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 2 and < 3 < 3 and < 4 < 4 and < 1 < 5 and < 6 Name other supplementary pairs: < 6 and < 7 < 7 and < 8 < 8 and < 5

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 1 and < 3 are called VERTICAL ANGLES They are congruent m<1 = m<3

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 2 and < 4 < 6 and < 8 Name other vertical pairs: < 5 and < 7

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 1 and < 5 are called CORRESPONDING ANGLES They are congruent m<1 = m<5 Corresponding angles occupy the same position on the top and bottom parallel lines.

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 2 and < 6 < 3 and < 7 Name other corresponding pairs: < 4 and < 8

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 4 and < 6 are called ALTERNATE INTERIOR ANGLES They are congruent m<4 = m<6 Alternate Interior on on the inside of the two parallel lines and on opposite sides of the transversal.

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 3 and < 5 Name other alternate interior pairs:

Parallel lines cut by a transversal 2 1 3 4 6 5 7 8 < 2 and < 8 < 1 and < 7 Name other alternate exterior pairs:

TRY IT OUT 2 1 3 4 6 5 7 8 120 degrees The m < 1 is 60 degrees. What is the m<2 ? 120 degrees

TRY IT OUT 2 1 3 4 6 5 7 8 60 degrees The m < 1 is 60 degrees. What is the m<5 ? 60 degrees

TRY IT OUT 2 1 3 4 6 5 7 8 60 degrees The m < 1 is 60 degrees. What is the m<3 ? 60 degrees

TRY IT OUT 120 60 60 120 120 60 60 120

TRY IT OUT 2x + 20 x + 10 What do you know about the angles? Write the equation. Solve for x. SUPPLEMENTARY 2x + 20 + x + 10 = 180 3x + 30 = 180 3x = 150 x = 30

TRY IT OUT 3x - 120 2x - 60 What do you know about the angles? Write the equation. Solve for x. ALTERNATE INTERIOR 3x - 120 = 2x - 60 x = 60 Subtract 2x from both sides Add 120 to both sides