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AssignmentMultiple Select

Triangles and Their Side Lengths

Question 1 • AZ-Geometry A (MA201)

Under which angle conditions could a triangle exist? Check all that apply.3 acute angles2 acute angles, 1 right angle1 acute angle, 1 right angle, 1 obtuse angle1 acute angle, 2 obtuse angles 2 acute angles, 1 obtuse angle

Answer
A
3 acute angles
B
2 acute angles, 1 right angle
C
1 acute angle, 1 right angle, 1 obtuse angle
D
1 acute angle, 2 obtuse angles
E
2 acute angles, 1 obtuse angle

Explanation

A triangle’s interior angles must add up to 180°. Three acute angles can do this, such as 60° + 60° + 60°, and two acute angles plus a right angle can do it, such as 45° + 45° + 90°. Two acute angles and an obtuse angle can also add to 180°, such as 40° + 40° + 100°. The choices with a right angle and an obtuse angle, or with two obtuse angles, are impossible because those angles alone add to more than 180°.

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