Triangle Properties Review

If two angles in a triangle are 95° and 32°, what is the measure of the third angle?

• 53°

• 45°

• 60°

• 90°

Answer explanation

The sum of angles in a triangle is 180°. Adding the two given angles: 95° + 32° = 127°. Subtracting from 180° gives the third angle: 180° - 127° = 53°. Thus, the measure of the third angle is 53°.

Tags

CCSS.HSG.CO.C.10

In a triangle, if one angle is 30° and another is 60°, what is the measure of the third angle?

• 60°

• 70°

• 80°

• 90°

Answer explanation

In a triangle, the sum of all angles is 180°. Given angles of 30° and 60°, the third angle is calculated as 180° - 30° - 60° = 90°. Therefore, the measure of the third angle is 90°.

Tags

CCSS.HSG.CO.C.10

Which of the following is a correct statement about triangle side lengths?

• 3, 5, and 10 can form a triangle.

• 3, 4, and 5 cannot form a triangle.

• 3, 5, and 10 cannot form a triangle.

Answer explanation

The triangle inequality states that the sum of the lengths of any two sides must be greater than the length of the third side. For 3, 5, and 10, 3 + 5 = 8, which is not greater than 10, so they cannot form a triangle.

Tags

CCSS.7.G.A.2

Which of the following sets of lengths cannot form a triangle?

• 7 feet, 2 feet, 9 feet

• 5 cm, 10 cm, 12 cm

• √10, 2 1/2, 5

Answer explanation

The lengths 7 feet, 2 feet, and 9 feet cannot form a triangle because they violate the triangle inequality theorem: 7 + 2 is not greater than 9.

Tags

CCSS.HSG.CO.C.10

What type of triangle has three congruent sides?

• Scalene triangle

• Isosceles triangle

• Equilateral triangle

• Right triangle

Answer explanation

An equilateral triangle has three congruent sides, meaning all sides are of equal length. In contrast, a scalene triangle has no congruent sides, and an isosceles triangle has exactly two congruent sides. A right triangle is defined by having a right angle.

Tags

CCSS.4.G.A.2

Which triangle has one obtuse angle?

• Right triangle

• Acute triangle

• Obtuse triangle

• Equilateral triangle

Answer explanation

An obtuse triangle is defined as having one angle greater than 90 degrees, making it the only type of triangle that can have an obtuse angle. In contrast, right triangles have one 90-degree angle, and acute triangles have all angles less than 90 degrees.

Tags

CCSS.4.G.A.2

Which triangle has a right angle?

• A

• C

• D

• B

Answer explanation

Triangle C has a right angle, which is characterized by one angle measuring 90 degrees. The other triangles (A, B, D) do not have a right angle, making C the correct choice.

Tags

CCSS.HSG.SRT.B.4

Which classification matches the triangle?

• Right isosceles triangle

• Acute scalene triangle

• Obtuse scalene triangle

• Equilateral triangle

Answer explanation

Triangle (E) is classified as a right isosceles triangle because it has one right angle and two equal sides, fitting the definition perfectly. The other options do not match its properties.

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

What do the interior angles in a triangle have a sum of?

• 180

• 90

• 360

• 270

Answer explanation

The sum of the interior angles in a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry, making '180' the correct answer.

Tags

CCSS.HSG.CO.C.10

Which angle measurements do NOT create a triangle?

• 60,60,60

• 90,45,45

• 50,60,40

• 50,100,30

Answer explanation

The angles 50, 60, and 40 sum to 150 degrees, which is less than 180 degrees.

Tags

CCSS.HSG.CO.C.10