Download Proof using similar right triangles:

PYTHAGOREAN THEOREM PROOF
Proof using similar right triangles:
Follow the steps below tocomplete the proof.
1.
Copy the right triangle with altitude
(height) CD.
A
b
a
There are two smaller triangles inside and the large right triangle on the outside. To make
the proof easier, draw the triangles separately and relabel their angles and sides. Only use
the labels from the original triangle above. They are started for you below.
7 ,,,
3.
,
D
Why are the three triangles similar?
Since the three triangles are similar, we can write ratios for the corresponding sides. Fill in
the question marks in the equations below.
Relating the large and medium triangles: a f
c = -~ ,.which can be rewritten as cf = 9
Relating the lm’ge and small triangles:
b ? can be rewritten as b2 = ?
- = which
c b’
5.
Now, by using substitution, az + b:~ = ~ + ~.
6.
By factoring, a~ + b2 = c(~ + __.). By looldng at the original triangle, (f + e) = ?
7.
Using substitution again, a2 + b2 --- c(~) = ~.
CCSS Geometry Connections Supplemental Materials, V1,1
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