Transcript Ratios and Proportions

Similarity in Right Triangles
Geometry
Unit 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:
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We will be discovering ways to prove
triangles similar.
You will need:
ruler
long straight edge (ex. Planner)
paper
scissors
Step 1:

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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:
Shorter side
2
longer side
3
1

Label the other 2 triangles as so:
5
4 6
7
8
9
Step 4:

Compare the angles of all three
triangles by placing them on top of
each other.
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Which s and  to 1?
Which s and  to 2?
Which s and  to 3?
What is true about all 3 triangles?
Step 5:
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Find the similarity ratio between the
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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:


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Original: AB middle:___
BD
DC
Original: BC middle:___
BC
Original: AC middle:___
AD
small: ___
DB
small: ___
AB
small: ___
Write a Similarity Statement
for the following picture:


ABC ~ ______ ~ ______
ABC ~ BDC ~ ADB