Lesson 8

Triangles with 3 Common Measures

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Problem 1

Are these two triangles identical? Explain how you know.

Two triangles, each with angles labeled 95 & 70 degrees.  First triangle, the side opposite the 70 degree angle is labeled 12.  Second triangle, the side opposite the 95 degree angle is labeled 12.

Solution

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Problem 2

Are these triangles identical? Explain your reasoning.

Two triangles are shown that share one side.

 

Solution

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Problem 3

Tyler claims that if two triangles each have a side length of 11 units and a side length of 8 units, and also an angle measuring \(100^\circ\), they must be identical to each other. Do you agree? Explain your reasoning.

Solution

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Problem 4

The markings on the number line are equally spaced. Label the other markings on the number line.

A blank number line with 9 evenly spaced tick marks. Starting on the left, the third tick mark is labeled negative 3, the fourth tick mark is labeled 0, and the sixth tick mark is labeled 6.

Solution

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(From Unit 5, Lesson 8.)

Problem 5

A passenger on a ship dropped his camera into the ocean. If it is descending at a rate of -4.2 meters per second, how long until it hits the bottom of the ocean, which is at -1,875 meters? 

Solution

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(From Unit 5, Lesson 9.)

Problem 6

Apples cost $1.99 per pound.

  1. How much do \(3 \frac{1}{4}\) pounds of apples cost?
  2. How much do \(x\) pounds of apples cost?
  3. Clare spent $5.17 on apples. How many pounds of apples did Clare buy?

Solution

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(From Unit 4, Lesson 3.)

Problem 7

Diego has a glue stick with a diameter of 0.7 inches. He sets it down 3.5 inches away from the edge of the table, but it rolls onto the floor. How many rotations did the glue stick make before it fell off of the table?

Solution

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(From Unit 3, Lesson 5.)