Math: Properties of Triangles Angles and Side Lengths Worksheet

Question 1

A triangle has side lengths of 6 cm, 6 cm, and 4 cm. What type of triangle is it by side lengths?

Accepted Answer

The triangle is an isosceles triangle because it has exactly two equal side lengths, 6 cm and 6 cm.

Question 2

A triangle has angles of 60 degrees, 60 degrees, and 60 degrees. What type of triangle is it by angles?

Accepted Answer

The triangle is an acute triangle because all three angles are less than 90 degrees.

Question 3

Two angles of a triangle measure 45 degrees and 65 degrees. What is the measure of the third angle?

Accepted Answer

The third angle measures 70 degrees because the angles in a triangle add to 180 degrees, and 180 - 45 - 65 = 70.

Question 4

A triangle has side lengths of 5 inches, 5 inches, and 5 inches. What type of triangle is it by side lengths?

Accepted Answer

The triangle is an equilateral triangle because all three side lengths are equal.

Question 5

Can side lengths of 3 cm, 4 cm, and 8 cm make a triangle? Explain your answer.

Accepted Answer

No, these side lengths cannot make a triangle because 3 + 4 = 7, and 7 is not greater than 8.

Question 6

A triangle has one angle that measures 90 degrees. What type of triangle is it by angles?

Accepted Answer

The triangle is a right triangle because it has one angle that measures exactly 90 degrees.

Question 7

A triangle has angles of 30 degrees, 50 degrees, and 100 degrees. What type of triangle is it by angles?

Accepted Answer

The triangle is an obtuse triangle because it has one angle that is greater than 90 degrees.

Question 8

Can side lengths of 7 cm, 9 cm, and 12 cm make a triangle? Explain your answer.

Accepted Answer

Yes, these side lengths can make a triangle because 7 + 9 = 16, and 16 is greater than 12.

Question 9

A triangle has side lengths of 4 m, 6 m, and 8 m. What type of triangle is it by side lengths?

Accepted Answer

The triangle is a scalene triangle because all three side lengths are different.

Question 10

Two angles of a triangle measure 25 degrees and 95 degrees. What is the measure of the third angle?

Accepted Answer

The third angle measures 60 degrees because 25 + 95 = 120, and 180 - 120 = 60.

Question 11

Look at a triangle with sides labeled 10 cm, 10 cm, and 16 cm. Which two sides are equal, and what does that tell you about the triangle?

Accepted Answer

The two sides that are 10 cm are equal, so the triangle is an isosceles triangle.

Question 12

A triangle has angles of 40 degrees, 70 degrees, and 70 degrees. What type of triangle is it by angles, and what type is it by side lengths?

Accepted Answer

The triangle is an acute triangle because all three angles are less than 90 degrees. It is also an isosceles triangle because two angles are equal, so the sides across from them are equal.

Question 13

A triangle has one angle of 110 degrees. Can this triangle also have a right angle? Explain.

Accepted Answer

No, it cannot also have a right angle because 110 degrees + 90 degrees = 200 degrees, which is more than the 180 degrees allowed in a triangle.

Question 14

Can side lengths of 5 units, 5 units, and 10 units make a triangle? Explain your answer.

Accepted Answer

No, these side lengths cannot make a triangle because 5 + 5 = 10, and the sum must be greater than the longest side, not equal to it.

Question 15

A triangle has two equal sides and one angle that measures 90 degrees. What can you say about this triangle?

Accepted Answer

This triangle is both an isosceles triangle and a right triangle because it has two equal sides and one right angle.

Math: Properties of Triangles Angles and Side Lengths

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