AnswersAZ-Geometry A MA201Triangles and Their Side Lengths

Lesson 2: Triangles and Their Side Lengths Answers

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111202

Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true?

A
This triangle exists because the sum of any two side lengths is greater than the length of the third side.
B
This triangle exists because the sum of 4 and 12 is less than 17.
C
This triangle does not exist because the sum of any two side lengths is greater than the length of the third side.
D
This triangle does not exist because the sum of 4 and 12 is less than 17.
111205

Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.

Answer:

According to the Triangle Inequality Theorem, the sum of any two side lengths of a triangle must be greater than the length of the third side. Because Ruben cut one dowel into two pieces, the sum of those two pieces is equal to the length of the uncut dowel. Since the sum is not greater than the third side, a triangle cannot be formed.

111206

What did you include in your response? Check all that apply.

A
The sum of the lengths of the two cut pieces is equal to the length of the long piece.
B
The sum of the lengths of the two cut pieces must be longer than the length of the long piece.

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