Math 2
Name _________________________________
Lesson 4-3: Proving Triangle Similarity, Part 1
 I can prove two triangles are similar, and understand similarity as a special case of congruence.
Read the following definition of terms that you learned in Math 1. Draw a picture of each term in order to
demonstrate your understanding of each term.
Picture
Vertical Angles: Non-adjacent, non-overlapping angles formed
by two intersecting lines
Linear Pair: Two supplementary angles that share a common vertex
and a common side
Supplementary angles: Two angles whose measures add up to
exactly 180 degrees
Complementary Angles: Two angles whose measures add up to
exactly 90 degrees
Perpendicular Lines: Two lines that intersect to form right angles
(can also have perpendicular rays and segments)
Corresponding Angles: Two angles that lie on the same side of a transversal, in corresponding positions with
respect to the two lines that the transversal intersects. If the transversal intersect parallel lines, corresponding angles
are congruent. Angles _____ and ______ in the above figure are an example of corresponding angles.
Same Side Exterior Angles: Two angles that lie on the same side of a transversal not between the two lines that the
transversal intersects. If the transversal intersect parallel lines, same side exterior angles are supplementary. Angles
_____ and ______ in the above figure are an example of same side exterior angles.
Same Side Interior Angles: Two angles that lie on the same side of a transversal between the two lines that the
transversal intersects. If the transversal intersect parallel lines, same side interior angles are supplementary.
Angles _____ and ______ in the above figure are an example of same side interior angles.
Alternate Interior Angles: Two angles that lie on opposite sides of a transversal between the two lines that the
transversal intersects – they do NOT form a linear pair. If the transversal intersect parallel lines, alternate interior
angles are congruent. Angles _____ and ______ in the above figure are an example of alternate interior angles.
Alternate Exterior Angles: Two angles that lie on opposite sides of a transversal not between the two lines that the
transversal intersects. If the transversal intersect parallel lines, alternate exterior angles are congruent.
Angles _____ and ______ in the above figure are an example of alternate exterior angles.
Apply the definitions above to solve for the angles in the below problems.
22.
In Math 1 you learned how to prove two triangles are congruent. In order to prove two triangles are
congruent. For two triangles to be congruent, all corresponding sides and angles must be congruent.
Proving all three sides and all three angles congruent would be time consuming. You learned three
congruence theorems that were “shortcuts” to proving congruence. What were the three theorems?
Triangle Similarity Theorems:
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Similarity Statement: ___________________________
If ALL of the sides of two triangles are in proportion, then the triangles are similar.
Similarity Statement: ___________________________
If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles
are in proportion, then the triangles are similar
Similarity Statement: __________________________
The below triangles are all similar. Identify the Triangle Similarity Theorem that allows you to conclude that
the triangles are similar. If necessary, show work necessary to prove the sides are proportional.
1.
Similarity Statement: ________________________
Work:
2.
Similarity Statement: ________________________
Work:
3.
Similarity Statement: ________________________
Work: