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alternate exterior angles

Alternate Exterior angles sample problems.

two parallel lines  cut by transversal
Which of the following pairs of angles are alternate exterior angles if the two lines cut by the transversal are parallel?

A and F
A and E
E and F


answer alternate exterior angles
If angle E measures 60 degrees, what is the measure of angle B, if the two lines are parallel?

A. 120
B. Can't determine from information
C.60
answer 2 alternate exterior angles
Do alternate exterior angles have to be congruent? No they are congruent only when the lines being crossed are parallel.
Common Core Standard G.CO.9
Keywords: congruent angles, lines and angles,transversal,high school math


1. Alternate Exterior angles are located on opposite sides of the transversal, and are diagonal from one another.

2. They are outside the two lines. ( Outside the bun)​ In order to help visualize the difference between exterior and interior angles I think of a hamburger. See the picture below.








3. Alternate exterior angles are congruent. (equal angle measure) when the lines crossed by the transversal are parallel.












orange line

Alternate Exterior angles in real life

Check out these examples of alternate exterior angles in real life. Once you see these examples you will start to notice other examples all around you.
example from real life alternate exterior angle flag
parking lot real life example alternate exterior angle 1
alternate exterior angle real life example tennis racguet
car grill-alternate exterior angle
perpendicular transversal
Right Angle
hamburger illustrating alternate exterior angles
Common Core Standard G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Interior Angles (inside the bun)

Exterior Angles (outside the bun)

Transversal

orange line

Alternate Exterior Angles

alternate exterior angles are congruent
alternate exterior angles

Definition of transversal

A transversal is a line that cuts across  two or more lines. If it crosses the two lines at a right angle it is a perpendicular transversal.
transversal
  • A transversal is a line that intersects two other lines. These lines are often parallel, but this is not required.
  • Alternate exterior angles are congruent if the lines intercepted by the transversal are parallel.
  • The lines are parallel if alternate interior, alternate exterior, or corresponding angles are congruent.
  • Corresponding angles lie in the same position at each intersection.
  • Alternate interior angles lie between the lines cut by the transversal.
  • Alternate exterior angles lie outside the lines cut by the transversal.
  • Alternate interior angles create a Z 
  • Alternate interior angles are used to prove triangles are congruent by SAS, ASA, AAS
  • Alternate exterior angles are supplementary to the adjacent angles.

Perpendicular Transversal 
Transversal
Interesting facts about angles created by a transversal 
q = Transversal

A transversal is a line that cuts across two or more lines.

Lines a and b = Parallel Lines

Angles 1 and 2 and Angles 3 and 4
Congruent Alternate Exterior Angles

Angles 1 and 3 and Angles 4 and 2 
 Supplementary Exterior Angles (180 degrees)

What are alternate exterior angles? When two lines are crossed by a transversal, the angle pair on the outside of the lines is the alternate exterior angle. The two lines do not have to be parallel.

A transversal is a line that cuts across two or more lines.