What’s Your Angle?What’s Your Angle?What’s Your Angle?What’s Your Angle?

By By Kim DavisKim Davis

Background Vocabulary

• Plane: an infinite, flat surface.• Parallel lines: lines in a plane that

never meet. l l is the symbol for parallel lines.

• Transversals: lines that intersect two or more parallel lines.

More Vocabulary1. Congruent angles: two

angles that have equal measures.

2. Ray: part of a line that has an endpoint and extends forever.

3. Angles: two rays with a common endpoint.

Types of Angles

Acute : angles that measure less that 90°.

Right: angles that measure 90°.

Obtuse: angles that measure more than 90° and less than 180°

Straight: angles that measure 180°.

Complementary Angle

Two angles whose

measure add up

to 90°.

45°45°

Supplementary Angles

Two angles whose

measures add up

to 180°.

Supplementary Angles

Two angles whose

measures add up

to 180°.

90°90°

Congruent Angles

When a transversalintersects two parallellines, eight angles areformed.

2.

1.3. 4.

5. 6.

7. 8.

2.

1.

3. 4.

5. 6.7. 8.

Alternate Interior Angles

Angle 3 and Angle 6 are congruent angles. This means they have the same measure.

2.

1.

3. 4.

5. 6.7. 8.

Alternate Interior Angles

Angle 4 and Angle 5 are congruent angles.

The measure of angle 4 and themeasure of angle 6 are congruent

ANDThe measure of angle 3 and the measure of angle 5 are congruent.

NOTE

Alternate Interior Angles are on “alternate” sides and on the “interior” of the parallel lines.

2.

1.

3. 4.

5. 6.7. 8.

Vertical Angles

Angle 1 and Angle 4 are congruent angles.

2.

1.

3. 4.

5. 6.7. 8.

Vertical Angles

Angle 2 and Angle 3 are congruent angles.

2.

1.

3. 4.

5. 6.7. 8.

Vertical Angles

Angle 5 and Angle 8 are congruent angles.

2.

1.

3. 4.

5. 6.7. 8.

Vertical Angles

Angle 6 and Angle 7 are congruent angles.

The measures of Angle 1 and Angle 3 are congruent.

The measures of Angle 2 and Angle 4 are congruent.

The measures of Angle 5 and Angle 7 are congruent.

The measures of Angle 6 and Angle 8 are congruent.

NOTE

Vertical Angles are diagonally across from each other.

Corresponding Angles

These angles are a bit trickier. You have to imagine cutting your diagram apart, and then pasting one part on top of the other.

2.

1.

3. 4.

5. 6.7. 8.

Corresponding Angles

Angle 1 and Angle 5 are congruent angels.

2.

1.

3. 4.

5. 6.7. 8.

Corresponding Angles

Angle 2 and Angle 6 are congruent.

2.

1.

3. 4.

5. 6.7. 8.

Corresponding Angles

Angle 3 and Angle 7 are congruent angles.

2.

1.

3. 4.

5. 6.7. 8.

Corresponding Angles

Angle 4 and Angle 8 are congruent angles.

Angle 1 and Angle 5 are congruent.Angle 2 and Angle 6 are congruent.Angle 3 and Angle 7 are congruent.Angle 4 and Angle 8 are congruent.

Demonstrate Your Knowledge

Now that you’ve seen what is congruent, you can take the measurement of “1” angle and

figure out the others. Let’s try it!

2.

1.

3. 4.

5. 6.7. 8.

Angle 2 measures 110°. What do the other angles measure?