Lesson 09: The Converse | Unit 8: Pythagorean Theorem and Irrational Numbers

Multiple Select

Which of these triangles are definitely right triangles? (Note that not all triangles are drawn to scale.)

• Triangle A

• Triangle B

• Triangle C

• Triangle D

• Triangle E

Open Ended

Explain how you know which triangles are definitely right triangles. (Note that not all triangles are drawn to scale.)

Open Ended

A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasoning.

Multiple Choice

Select **all** the sets that are the three side lengths of right triangles.

• 8, 7, 15

• 4, 10, $$\sqrt{84}$$

• $$\sqrt{8}$$ , 11, $$\sqrt{129}$$

• $$\sqrt{1}$$ , 2, $$\sqrt{3}$$

Multiple Choice

Which of the following objects contains a right angle?

• Squares and rectangles contain right angles.
• Ovals are defined by right angles.
• Triangles always have right angles.
• Circles contain right angles.

Open Ended

Measure the two sides that make the right angle of the object you found. Then measure the distance from the end of one side to the end of the other. Provide the measurements.

Draw

Draw a diagram of the object you found, including the measurements of the sides and the distance between them.

Open Ended

Use the Pythagorean Theorem to show that your object really does have a right angle. Explain your reasoning.

Open Ended

Is the shaded triangle a right triangle? Explain or show your reasoning.