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Alternate Interior Angles - Problem 2

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Given two parallel lines and a transversal, there are alternate interior angles. Remember that alternate interior angles are congruent. So, two angles on opposite and interior (meaning between the parallel lines) sides of a transversal crossing two parallel lines are congruent. This can be used to find the measure of these angles.

Alternate interior angles can be used along with vertical angles, corresponding angles, or other angle concepts, in order to find the measure of a given angle.

When we have two parallel lines that are intersected by a transversal and again my parallel lines I identified by using the same number of arrows, then two specials angles are congruent and that is alternate interior angles, so let’s examine these two words.

Alternate means on opposite sides, interior means within, or in between. So here we have our two parallel lines, our alternate interior angles are going to be the angles that are inside, and on opposite sides of the transversal. So angle 4 is inside, and its opposite side would be 6, so those two angles will be congruent.

There’s only one other pair of alternate interior angles and that’s angle 3 and it’s opposite side in between the parallel lines which is 5. So alternate interior angles will always be congruent and they’ll always be on opposite sides of this transversal.

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