Question

In the figure below, there are three right trangles. Complete the following.
(a) Write a similiarity statement relating the three right triangles.

(b) Complete each proportion.

Answer 1

a. The similarity statement that relates the three right triangles is: ΔEGF ~ ΔGHF ~ ΔEHG

b. EF/EG = EG/EH; HF/HG = GH/EH

Facts about Similar Triangles

• Based on the similar right triangle theorem, if an altitude of a right triangle is drawn from the right  angle of a right triangle, two right triangles are formed which are similar to each other and also both similar right triangles are similar to the original right triangle. In essence, all three right triangles are similar.

• Similar triangles have three pairs of corresponding side lengths whose ratio are equal, that is, their corresponding side lengths are proportional to each other.

• When writing similarity statement, the corresponding side lengths are taken into consideration.

a. Therefore, the similarity statement that relates the three right triangles is: ΔEGF ~ ΔGHF ~ ΔEHG

b. The proportion of their corresponding sides will be:

EF/EG = EG/EH

HF/HG = GH/EH

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