Lesson 16

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

  1. Draw segment \(PQ\).
  2. When \(PQ\) is rotated \(180^\circ\) around point \(R\), the resulting segment is the same as \(PQ\). Where could point \(R\) be located?

Solution

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(From Unit 1, Lesson 7.)

Problem 5

Here is trapezoid \(ABCD\).

Trapezoid \(A\ B\ C\ D\). Upper and lower sides are parallel. Upper and lower left angles are right angles. Upper right angle is 120 degrees and lower right angle is 60 degrees.

 

Using rigid transformations on the trapezoid, build a pattern. Describe some of the rigid transformations you used.

Solution

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(From Unit 1, Lesson 9.)