IM 8.8.9 Lesson: The Converse
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.
Over the course of a day:
What is the farthest apart the two tips get?
What is the closest the two tips get?
Are the two tips ever exactly five centimeters apart?
Here are three triangles with two side lengths measuring 3 and 4 units, and the third side of unknown length. Sort the following six numbers from smallest to largest. Put an equal sign between any you know to be equal.
Explain your reasoning.
A related argument also lets us distinguish acute from obtuse triangles using only their side lengths.
Decide if triangles with the following side lengths are acute, right, or obtuse. In right or obtuse triangles, identify which side length is opposite the right or obtuse angle. , ,
, ,
, ,
Given the information provided for the right triangles shown here, find the unknown leg lengths to the nearest tenth.
Sketch these new right triangles, and clearly label the right angle.
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?
