### Home > INT2 > Chapter 7 > Lesson 7.1.4 > Problem 7-51

7-51.

Examine the diagram at right.

Are the triangles in this diagram similar? Justify your answer using similarity transformations.

Draw

and separately. Which angles are congruent? What is the relationship between the lengths

and? Between the lengthsand? Between the lengthsand?Compare

with. How are these lengths related? If the triangles are similar,

then this relationship will be true for the other pairs of corresponding sides.If

units andunits, what is?Add the lengths to your diagram from part (a). If

, how long is?

Use the Pythagorean Theorem to calculate the unknown side length.