Unit 1

Angles formed by parallel lines.Standards MCC8G1-5

The angles created when Parallel Lines Are Cut By A Transversal:

• Alternate Interior Angles (congruent)• Alternate Exterior Angles (congruent)• Corresponding Angles (congruent)• Vertical Angles (congruent)

• Consecutive Interior Angles (sum to 180°)• Supplementary Angles (sum to 180°)

Similar Triangles• If two triangles have two congruent angle

measures, then the triangles are similar.

45°45°

50° 50°

Exterior Angles of a Triangle An exterior angle of a triangle is formed by any side of a triangle and the extension of its adjacent side. The Exterior Angle Theorem states thatAn exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Adapted from the Arizona Department of Education

• Show that m 3 ∠ + m 4 ∠ + m 5 ∠ = 180˚,

given that lines l and m are parallel lines

and t1 & t2 are transversals.

• Find the m a∠ , m b ∠ , and the m c∠if line n and segment yz are parallel.

n

If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67° 23°

1 2

t

s

Examples & Explanations

If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67° 23°

1 2

t

s

Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67°

23°

1 2

t

s

Examples & Explanations

If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67°

23°

1 2

t

s

Examples & Explanations

If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67°23°

1 2

t

s

Examples & ExplanationsIf lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67°23°

1 2

t

s

Examples & Explanations

If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2.

m

n

p

67° 23°

23° 67°

t

s