Similarity in Right Triangles

GeometryUnit 11, Day 7

Ms. Reed

Similarity in Right Triangles Right Triangles have specific

relationships with the lengths of the legs, the hypotenuse and the altitude.

In groups of 2: We will be discovering ways to

prove triangles similar. You will need:

rulerlong straight edge (ex.

Planner) paperscissors

Step 1: Draw one diagonal on the piece of

paper This should form 2 congruent

triangles If congruent, cut the paper along

the line of the diagonal.

Step 2: Fold the triangle to find the

altitude so that the altitude intersects the hypotenuse.

Once done correctly, cut along the altitude to create 2 more triangles.

Step 3: Label the bigger triangle as so:

Label the other 2 triangles as so:

2

1 3

Shorter side longer side

4

5

6

7

8 9

Step 4: Compare the angles of all three

triangles by placing them on top of each other. Which s and to 1? Which s and to 2? Which s and to 3?

What is true about all 3 triangles?

Step 5: Find the similarity ratio between

the Smallest triangle to the middle

triangle Middle triangle to the largest triangle Smallest triangle to largest triangle

What we discovered! The altitude to the hypotenuse of a

right triangle divides the triangle into 2 triangles, making all 3 triangles similar.

Name the corresponding sides for the following picture: Original: AB middle:___ small:

___ Original: BC middle:___ small:

___ Original: AC middle:___ small:

___

DB

AD

DC

BD

BC AB

Write a Similarity Statement for the following picture: ABC ~ ______ ~ ______ ABC ~ BDC ~ ADB