What’s Your Angle?.

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Presentation transcript:

What’s Your Angle?

Background Vocabulary plane: an infinite, flat surface angles: two rays with a common endpoint congruent angles: two angles that have equal measures transversals: lines that intersect two or more lines (It’s the one line that both angles are touching.) parallel lines: lines in a plane that never meet. l l is the symbol for parallel lines.

Complementary Angles Two angles whose measure add up to 90°. 35° 55°

Supplementary Angles Two angles whose measures add up to 180°. 90° 90°

Vertical Angles Vertical angles are diagonally across from each other. Vertical angles are congruent.

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

Relationships Matter When a transversal crosses two PARALLEL lines, we can say a lot about their angle measures.

When lines are parallel: 1. 2. 3. 4. 5. 6. 7. 8. = indicates lines are parallel

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

Alternate Interior Angles Alternate interior angles are congruent. 1. 2. 3. 4. 5. 6. 7. 8. Angle 3 and Angle 6 are congruent angles. This means they have the same measure.

Alternate Exterior Angles Alternate exterior angles are on “alternate” (opposite) sides and on the “exterior” (outside) of the parallel lines.

Alternate Exterior Angles Alternate exterior angles are congruent. 1. 2. 3. 4. 5. 6. 7. 8. Angle 1 and Angle 8 are congruent angles. This means they have the same measure.

Corresponding Angles Corresponding angles are in the same relative location.

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

Consecutive Interior Angles Consecutive interior angles are next to each other (on the same side of the transversal) between the lines.

Consecutive Interior Angles Consecutive interior angles are SUPPLEMENTARY. 1. 2. 3. 4. 5. 6. 7. 8. Angle 4 and Angle 6 are supplementary angles. Together their measures = 180°

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??

Answers 70° 110° 110° 70° 70° 110° 70° 110°

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