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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
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!