Name: __________________________
Using Similar Triangles to Prove a Product
Date:_____ Period:____
Ms. Anderle
Using Similar Triangles to Prove Proportions
To prove that the product of the means equals the product of the extremes in a
geometric proportion, all that we need to do is follow this easy method below!
1) Rewrite the products as a proportion, using one pair as the means and the
other pair as the extremes.
2) Determine the triangles that need to be proved similar by reading the
proportions and marking the given figures.
3) Complete the proof the same as we did the other day. Adding the product
as the last step. In order to prove the product of the means equal to the
product of the extremes, this reason is used: “In a proportion, the
product of the means equals the product of the extremes.”
4) Your proof is complete!!! 
***If the product happens to be a square,
write the proportion as a mean proportional***
Example:
Q
R
A
P
Given: PQ || SR
Prove: QP x RA = RS x PA
S
2)
A
D
Given: DE || BC
E
B
Prove: AD x AC = AB x AE
C
3)
A
Given: <ABE ≅ <ADC
Prove: AB x AC = AD x AE
B
D
F
C
E
Now Try: page 320 # 5, 8, 10