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IM Geo.3.14 Practice: Proving the Pythagorean Theorem

Which of the following are right triangles?

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In right triangle ABC, a square is drawn on each of its sides.

An altitude  is drawn to the hypotenuse  and extended to the opposite side of the square on . In class, we discussed Elena’s observation that  and Diego’s observation that . Mai observes that these statements can be thought of as claims about the areas of rectangles. Which rectangle has the same area as ?

Which rectangle has the same area as ?

In the applet below, Andre says he can find the length of the third side of triangle and it is 5 units. Mai disagrees and thinks that the side length is unknown. Do you agree with either of them? Show or explain your reasoning.

In right triangle ABC, altitude CD is drawn to its hypotenuse.

Find 2 triangles which must be similar to triangle .

In right triangle , altitude with length 6 is drawn to its hypotenuse. We also know . What is the length of ?

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Lines  and  are both vertical. What is the length of ?

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In right triangle , and . A new triangle  is formed by connecting the midpoints of  and . What is the area of triangle ?

What is the area of triangle ?

Does the scale factor for the side lengths apply to the area as well?  

Quadrilaterals and are similar. What is the scale factor of the dilation that takes  to ?

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Priya is trying to determine if triangle ADC is congruent to triangle CBA.

She knows that segments  and  are congruent She also knows that angles  and  are congruent. Does she have enough information to determine that the triangles are congruent?