Triangle Angle Theorems Answers

✔ acuteobtuseright

less than✔ equal togreater than

acuteobtuseX right

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CECAAE

segment addition postulatesubstitution propertytransitive property

If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.Triangle LMN is an obtuse triangle.The angle at vertex L is acute.The angle at vertex L is right.The angle at vertex N is right. The angle at vertex N is acute.Triangle LMN is a right triangle.

Angle X must be .

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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.

3005007001,000

CECAAE

Angle Z must be .

< d <

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.

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

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.