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Naomi used the figure shown to help prove the Pythagorean Theorem. In the figure, both △ACD and △CBD are similar to △ABC.

Triangle ABC. Point D lies on side AB. Segment CD is shown. Angle ACB and angle CDB each have a square angle marker. Side BC is labeled lowercase a. Side AC is labeled lowercase b. Side AB is labeled lowercase c. Segment AD is labeled y. Segment DB is labeled x.

She began by correctly setting up the proportions ac=xa and bc=yb and cross-multiplying to get the equations a2=xc and b2=yc. What should Naomi do next?

Select from the drop-down lists to complete each sentence correctly.

First, she should find the
product
of the equations a2=xc and b2=yc to get another equation. Then she should factor one of the sides of the resulting equation. Finally, she should substitute
c
into the resulting equation and multiply. This will prove the Pythagorean Theorem.