Q4W2: Angles and Transversals. Objectives I understand why an exterior angle of a triangle is equal to the sum of the opposite interior angles. I understand.

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Presentation transcript:

Q4W2: Angles and Transversals

Objectives I understand why an exterior angle of a triangle is equal to the sum of the opposite interior angles. I understand the angle relationships that occur when parallel lines are cut be a transversal.

Vocabulary Supplementary Angles: Two angles that add up to 180 degrees. Together they form a straight line.

What is the measure of the missing angle?

Triangle Review The angles of a triangle always add up to 180 degrees.

Angles When the sides of a triangle are extended, other angles are formed:

Angles Knowing that supplementary angles always add up to 180, what is the missing angle?

Find the missing EXTERIOR angle. Note: Not to scale

External Angle Theorem

Exterior Angle Theorem

Using the Exterior Angle Theorem

Parallel Lines & Transversals What is a transversal? A transversal is a line that crosses at least two other lines.

Parallel Lines & Transversals When two parallel lines are cut by a transversal, pairs of congruent and supplementary angles are formed. In geometry, “congruent” means “same.”

Parallel Lines & Transversals Congruent Angles There are 4 types of congruent angles that are created when parallel lines are crossed by a transversal. 1. Vertical Angles 2. Alternate Interior Angles 3. Alternate Exterior Angles 4. Corresponding Angles

Vocabulary Vertical Angles: each of the pairs of opposite angles formed when parallel lines are crossed by a transversal.

Vocabulary Corresponding Angles: the angles that occupy the same relative position when parallel lines are crossed by a transversal.

Congruent Angles When parallel lines are crossed by a transversal, alternate interior and alternate exterior angles are also congruent!

Parallel Lines & Transversals Name the Congruent Angles 1. Vertical Angles: _____________________________ 2. Alternate Interior Angles: ___________________ 3. Alternate Exterior Angles: ___________________ 4. Corresponding Angles: ______________________

Fill in the missing angle measurements Due to all of these congruent and supplementary angles, if you know one angle measurement, you can name them all!

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