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Unit 8 - Lesson 9 - Grade 8: Illustrative Mathematics

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Last updated 2 months ago
7 Questions
Note from the author:
Grade 8 Unit 9
Lesson 9: The Converse
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 9
Lesson 9: The Converse
CC BY 2021 Illustrative Mathematics®
Lesson: The Converse

The Hands of a Clock (Warm Up)

Consider the tips of the hands of an analog clock that has an hour hand that is 3 centimeters long and a minute hand that is 4 centimeters long.

1.

Over the course of a day:
What is the farthest apart the two tips get?

2.

Over the course of a day:
What is the closest the two tips get?

3.

Over the course of a day:
Are the two tips ever exactly five centimeters apart?

Proving the Converse

Here are three triangles with two side lengths measuring 3 and 4 units, and the third side of unknown length.

4.

Sort the following six numbers from smallest to largest. Put an equal sign between any you know to be equal. Be ready to explain your reasoning.

1 5 7 x y z


Calculating Legs of Right Triangles

5.

Given the information provided for the right triangles shown here, find the unknown leg lengths to the nearest tenth.


6.

The triangle shown here is not a right triangle. What are two different ways you change one of the values so it would be a right triangle? Sketch these new right triangles, and clearly label the
right angle.

Cool Down: Is It a Right Triangle?

Is It a Right Triangle?

7.

The triangle has side lengths 7, 10, and 12. Is it a right triangle? Explain your reasoning.