Triangles and Their Side Lengths

Question 1

Angle X must be .

Revolt · Accepted Answer

acute

Question 2

Angle Z must be .

Revolt · Accepted Answer

acute

Question 3

The sum of angles X and Z must be 90°.

Revolt · Accepted Answer

equal to

Question 4

< d <

Revolt · Accepted Answer

300

Question 5

In triangle ABC, we can draw a perpendicular line segment from vertex C to segment AB. The intersection of AB and the perpendicular is called E. We know that BE is the shortest distance from B to and that is the shortest distance from A to CE because of the shortest distance theorem. Therefore, BC > BE and AC > AE. Next, add the inequalities: BC + AC > BE + AE. Then, BE + AE = BA because of the . Therefore, BC + AC > BA by substitution.

Revolt · Accepted Answer

CE

Question 6

< d <

Revolt · Accepted Answer

700

Question 7

In triangle ABC, we can draw a perpendicular line segment from vertex C to segment AB. The intersection of AB and the perpendicular is called E. We know that BE is the shortest distance from B to and that is the shortest distance from A to CE because of the shortest distance theorem. Therefore, BC > BE and AC > AE. Next, add the inequalities: BC + AC > BE + AE. Then, BE + AE = BA because of the . Therefore, BC + AC > BA by substitution.

Revolt · Accepted Answer

AE

Question 8

In triangle ABC, we can draw a perpendicular line segment from vertex C to segment AB. The intersection of AB and the perpendicular is called E. We know that BE is the shortest distance from B to and that is the shortest distance from A to CE because of the shortest distance theorem. Therefore, BC > BE and AC > AE. Next, add the inequalities: BC + AC > BE + AE. Then, BE + AE = BA because of the . Therefore, BC + AC > BA by substitution.

Revolt · Accepted Answer

segment addition postulate

Triangles and Their Side Lengths Answers

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