Question

(From Unit 4, Lesson 1.)
5. Clare and Han are discussing how to find the missing lengths. Clare says she is using
similarity. Han says he is using the Pythagorean Theorem.
a. Do you agree with either of them? Show or explain your reasoning.
b. Find the missing sides.

Answer 1

The values of the missing sides is DE = 12 and AC = 6.5

Similar triangles

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion. Also all the corresponding angles are congruent.

Using Pythagoras:

AC² = AB² + BC²

AC² = 2.5² + 6²

AC = 6.5

Using similar triangles:

BC / DE = AB / EF

6/DE = 2.5/5

DE = 12

The values of the missing sides is DE = 12 and AC = 6.5

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