Geometry Theorems About Triangles Quiz: 10 Questions with Explanations

A 70 degreesB 110 degreesC 80 degreesD 130 degrees

The angles add to 180, so 180 – 50 – 60 = 70. The value 110 is 50 + 60, the sum of the two known angles.

A 70 degreesB 110 degreesC 140 degreesD 180 degrees

The exterior angle equals the sum of the remote interior angles: 40 + 70 = 110.

A 50 degreesB 130 degreesC 80 degreesD 65 degrees

The base angles share 180 – 50 = 130, so each is 65 degrees.

A 26B 52C 13D 6.5

A midsegment is half as long as the parallel side, so 26 / 2 = 13.

A 3, 4, 8B 5, 5, 10C 7, 10, 12D 2, 6, 9

Only 7 + 10 > 12 and the other sums also work. In 5, 5, 10 the two short sides sum to exactly 10, not more.

A 7B 10.5C 21D 14

The centroid is 2/3 of the way from the vertex: 2/3 of 21 is 14. The distance 7 is from the midpoint of the side.

A (4, 4)B (6, 6)C (3, 3)D (4.5, 4.5)

Average the coordinates: (0 + 9 + 3)/3 = 4 and (0 + 3 + 9)/3 = 4.

A 3B 5C 19D 20

The third side must be between 11 – 8 = 3 and 11 + 8 = 19, not including the endpoints. Only 5 is inside the range.

A 120 degreesB 20 degreesC 40 degreesD 60 degrees

9x = 180 gives x = 20, so the largest angle is 6(20) = 120. The value 20 is x itself.

A 72 degreesB 36 degreesC 108 degreesD 18 degrees

Angle C is also 72, so angle A = 180 – 144 = 36 degrees.