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.
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[/img][br][size=150]Over the course of a day:[/size][br][br]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.[br][br][math]x=15[/math], [math]y=20[/math], [math]z=8[/math]
[math]x=8[/math], [math]y=15[/math], [math]z=13[/math]
[math]x=17[/math], [math]y=8[/math], [math]z=15[/math]
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?
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[/img]

IM 8.8.9 Practice: The Converse

Which of these triangles are definitely right triangles? Select all that apply.
[size=150](Note that not all triangles are drawn to scale.)[/size][br][img]data:image/png;base64,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[/img]
Explain how you know the triangles you identified are right triangles.
[size=150][size=100]A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasoning.[/size][/size][br][img]data:image/png;base64,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[/img]
[size=150]In each part, [math]a[/math] and [math]b[/math]represent the length of a leg of a right triangle, and [math]c[/math] represents the length of its hypotenuse. Find the missing length, given the other two lengths.[/size][br][br][math]a=12[/math], [math]b=5[/math], [math]c=?[/math]
[math]a=?[/math], [math]b=21[/math], [math]c=29[/math]
[size=150]For which triangle does the Pythagorean Theorem express the relationship between the lengths of its three sides?[/size][br][br][img]data:image/png;base64,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[/img]
[size=150][size=100]Andre makes a trip to Mexico. He exchanges some dollars for pesos at a rate of 20 pesos per dollar. While in Mexico, he spends 9000 pesos. When he returns, he exchanges his pesos for dollars (still at 20 pesos per dollar). He gets back [math]\frac{1}{10}[/math] the amount he started with. Find how many dollars Andre exchanged for pesos and explain your reasoning. If you get stuck, try writing an equation representing Andre’s trip using a variable for the number of dollars he exchanged.[/size][/size]

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