Angles formed by parallel lines cut by a transversal
Terms and Definitions
Vertical angles: Two angles across from each other on intersecting lines.
Adjacent Angles: Two angles that are next to each other and share a common side.
Complementary Angles: Any two angles whose sum is 90°.
Supplementary Angles: Any two angles whose sum is 180°.
Corresponding Angles: Congruent angles which are on the same side of the transversal.
Alternating Interior Angles: Congruent, interior angles which are on alternating sides of the
transversal.
Alternating Exterior Angles: Congruent, exterior angles which are on alternating sides of the
transversal.
Same Side Exterior Angles: Supplementary, exterior angles which are on the same side of the
transversal.
Same Side Interior Angles Supplementary, interior angles which are on the same side of the
transversal.
Linear Pair: Two angles that are adjacent and supplementary. They form a straight line.
Adjacent Angles: 1 and 2;
2 and 4; 4 and 3; 1 and 3; 5 and 6; 6 and 8; 8 and 7; 5 and 7
Vertical Angles: 8 and 5; 1 and 4; 2 and 3; 6 and 7
Corresponding Angles: 2 and 6; 4 and 8; 1 and 5; 3 and 7
Alternate Exterior Angles: 1 and 8 and 2 and 7
Same side Exterior Angles: 2 and 8; 1 and 7
Alternate Interior Angle: 3 and 6; 4 and 5
Same Side Interior Angles: 4 and 6; 3 and 5
Check out this link below:
Special Angles
https://www.mathsisfun.com/geometry/parallel-lines.html
Proof that Interior Angles of a Triangle is 180°
Check out this link: https://www.mathsisfun.com/proof180deg.html
Proof
This is a proof that the angles in a triangle equal 180°:
The top line (that touches the top of the triangle) is
running parallel to the base of the triangle.
So:


A are the same
angles B are the same
angles
And you can easily see that
A + C + B does a complete rotation from one
side of the straight line to the other, or 180°
Angle Angle Criterion Theorem:
Two triangles with two pairs of equal
corresponding angles are similar. (This is known as
the AA criterion for similarity.)
Check out additional links:
https://learnzillion.com/lesson_plans/7366-find-the-side-length-of-a-triangle-usingangle-angle-criterion#fndtn-lesson
https://www.engageny.org/.../geometry-m2-topic-c-lesson-15-teacher.pdf?
http://www.onlinemathlearning.com/aa-criterion-similar-triangles-hsg-srt3.html
Finding the measure of exterior angles
Check out link: https://www.mathsisfun.com/geometry/exterior-angles.html