Triangles and Their Side Lengths

Question 1

Under which angle conditions could a triangle exist? Check all that apply.

Revolt · Accepted Answer

3 acute angles; 2 acute angles, 1 right angle; 2 acute angles, 1 obtuse angle

Question 2

Question 4

Revolt · Accepted Answer

120

Question 3

Triangle DEF contains two congruent acute angles. The sum of the measures of the two congruent acute angles is greater than 90 degrees. Anna concludes that the triangle must be an acute triangle. Which best describes her conclusion?

Revolt · Accepted Answer

She is correct. The remaining angle of the triangle measures less than 90 degrees.

Question 4

Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles?

Revolt · Accepted Answer

2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.

Question 5

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C? How far would Pete walk if he went from A to B to C? yards The direct distance from A to C is more than yards. The inequality w < represents the distance, w, that Pete might save by taking the direct path.

Revolt · Accepted Answer

Part 1: 40; Part 2: 10; Part 3: 30

Question 6

A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n?

Revolt · Accepted Answer

15 < n < 25

Question 7

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

Revolt · Accepted Answer

This triangle does not exist because the sum of 4 and 12 is less than 17.

Question 8

In triangle ABC, AB measures 25 cm and AC measures 35 cm. The inequality < s < represents the possible third side length of the triangle, s, in centimeters. The inequality < p < represents the possible values for the perimeter, p, of the triangle, in centimeters.

Revolt · Accepted Answer

Part 1: 10; Part 2: 60; Part 3: 70; Part 4: 120

Question 9

In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.m∠R > 90°m∠S + m∠T m∠Tm∠R > m∠S m∠S > m∠T

Revolt · Accepted Answer

m∠R > 90°; m∠S + m∠T < 90°; m∠R > m∠T; m∠R > m∠S

Question 10

Question 14

Revolt · Accepted Answer

60

Triangles and Their Side Lengths Answers

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