Download Similar Triangles Name: Date: Supplementary Angles: Two angles

Geometry: Lesson 5
Similar Triangles
Name:__________________
Date:___________________
Supplementary Angles: Two angles whose sum is 180°.
Complementary Angles: Two angles which combine to make 90°.
Vertical Angles: The opposite angles formed by intersecting lines are congruent.
1. What does it mean for two triangles to be similar?
2. There are many different conditions that allow us to claim that two triangles are “similar.” The
easiest way is if the measures of the angles of one triangle are the same as another.
a)
[Read this as “Triangle AB-C is similar to Triangle D-E-F”]. Mark the
corresponding angles on the triangles to the right.
Geometry: Lesson 5
3. The sides of similar triangles are proportional, meaning there’s a ratio of growth/shrinkage
between one triangle to its similar partner.
a) Construct a proportion to solve for the unknown side.
b) Find the missing side lengths using proportions.
c) Find the value of x.
3. What if we only know two angles? Can we say that the triangles are similar? (Right now, we
are only saying that triangles are similar if all 3 angles are the same measurement). Fill in the
missing angles measures.
Geometry: Lesson 5
4. Based on what we’ve worked on in the past two problems, decide if each pair of triangles
below are congruent.
a)
b)
c)
d)
Geometry: Lesson 5
5. Applications of Similar Triangles: Imagine you’re on vacation in London, England with your
family. As you toured the city, you saw the Big Ben a little ways off and your mother decided you
should get a family picture taken with it in the background. You ask someone on the street to
take the picture for you. He decided to be “artsy” and kneeled down to get a good angle on the
photo. Unfortunately, when you checked the picture your father’s head covered up the Big Ben!
a) You can figure out the height of the Big Ben using similar triangles! You know that
you are about 930 feet away from the tower in the picture, and that the photographer
stood back about 12 feet to take it. Since he was kneeling down, the camera was about
2 feet above the ground. If your father is an even 6 feet tall, how tall is the tower? Draw a
diagram below to help you figure it out.
Reflection: Think of another scenario where similar triangles might be useful.