What’s Your Angle?

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 Vocabulary Congruent angles: two angles that have equal measures. Ray: part of a line that has an endpoint and extends forever. Angles: two rays with a common endpoint.

Types of Angles Acute : angles that measure less that 90°.

Right: angle that measures 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 Supplementary Angles Two angles whose measures add up to 180°. Two angles whose measures add up to 180°. 90° 90°

When a transversal intersects two parallel lines, eight angles are formed. 1. 2. 3. 4. 5. 6. 7. 8.

Alternate Interior (or generally just alternate) Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 3 and Angle 6 are congruent angles. This means they have the same measure.

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

Alternate Angles 1. 2. 3. 4. 5. 6. 8. 7. Angle 4 and Angle 5 are equal, and Angle 3 and Angle 6 are equal. Two pairs of equal alternate angles are formed when a transversal cuts parallel lines

RECAP SO.... The measure of angle 4 and the measure of angle 6 are congruent AND The 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.

Vertically Opposite Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 1 and Angle 4 are congruent angles.

Vertically Opposite Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 2 and Angle 3 are congruent angles.

Vertically Opposite Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 5 and Angle 8 are congruent angles.

Vertically Opposite Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 6 and Angle 7 are congruent angles.

Vertically Opposite Angles 1. 2. 3. 4. 5. 6. 7. 8. Four pairs of vertically opposite angles are formed when a transversal cuts parallel lines: Angle 1 and Angle 4, Angle 2 and Angle 3, Angle 5 and Angle 8, and Angle 6 and Angle 7.

RECAP The measures of Angle 1 and Angle 3 are congruent.

Vertically opposite Angles are diagonally across from each other. NOTE Vertically opposite 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.

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

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

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

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

Corresponding Angles 1. 2. 3. 4. 5. 6. 7. 8. Four pairs of equal,corresponding angles are formed when a transversal crosses parallel lines: Angle 1 and Angle 5, Angle 2 and Angle 6, Angle 3 and Angle 7, and Angle 4 and Angle 8.

RECAP Angle 1 and Angle 5 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!

WHY?? Angle 2 measures 110°. What do the other angles measure? 1. 2. 3. 4. 5. 6. 7. 8. WHY??