Geometry: Triangles (High School) Worksheet

Question 1

In triangle ABC, angle A measures 42 degrees and angle B measures 68 degrees. Find the measure of angle C.

Accepted Answer

Angle C measures 70 degrees because the angles in a triangle add to 180 degrees, and 180 - 42 - 68 = 70.

Question 2

A triangle has side lengths 7 cm, 10 cm, and 15 cm. Determine whether these lengths can form a triangle. Explain your reasoning.

Accepted Answer

Yes, the lengths can form a triangle because the sum of any two side lengths is greater than the third side: 7 + 10 > 15, 7 + 15 > 10, and 10 + 15 > 7.

Question 3

Classify a triangle with side lengths 9, 9, and 14 by its sides and by its angles.

Accepted Answer

The triangle is isosceles because it has two equal sides. Since 14 squared is 196 and 9 squared plus 9 squared is 162, the triangle is obtuse because the square of the longest side is greater than the sum of the squares of the other two sides.

Question 4

In triangle DEF, DE is congruent to DF. If angle E measures 54 degrees, find the measures of angles D and F.

Accepted Answer

Angle F measures 54 degrees because base angles of an isosceles triangle are congruent. Angle D measures 72 degrees because 180 - 54 - 54 = 72.

Question 5

Two triangles have side lengths 6, 8, 10 and 9, 12, 15. Are the triangles similar? Explain.

Accepted Answer

Yes, the triangles are similar because the corresponding side lengths are proportional. The scale factor from the first triangle to the second is 1.5 since 9/6 = 12/8 = 15/10 = 1.5.

Question 6

A right triangle has legs of length 12 inches and 16 inches. Find the length of the hypotenuse.

Accepted Answer

The hypotenuse is 20 inches because 12 squared plus 16 squared equals 144 + 256 = 400, and the square root of 400 is 20.

Question 7

A right triangle has a hypotenuse of 13 meters and one leg of 5 meters. Find the length of the other leg.

Accepted Answer

The other leg is 12 meters because 5 squared plus b squared equals 13 squared, so 25 + b squared = 169, b squared = 144, and b = 12.

Question 8

Find the area of a triangle with a base of 18 cm and a height of 7 cm.

Accepted Answer

The area is 63 square centimeters because the area of a triangle is one half times base times height, so one half times 18 times 7 equals 63.

Question 9

Triangle JKL is congruent to triangle MNO. The congruence statement is triangle JKL congruent to triangle MNO. If angle K measures 47 degrees, which angle in triangle MNO is congruent to angle K, and what is its measure?

Accepted Answer

Angle N is congruent to angle K, so angle N measures 47 degrees. The order of the letters in the congruence statement shows the corresponding vertices.

Question 10

Decide whether the triangles are congruent. Triangle ABC has AB = 5, AC = 8, and angle A = 60 degrees. Triangle DEF has DE = 5, DF = 8, and angle D = 60 degrees. Explain which congruence theorem applies.

Accepted Answer

The triangles are congruent by SAS because two corresponding sides and the included angle between them are congruent.

Question 11

A 30-60-90 triangle has a shorter leg of 6 units. Find the longer leg and the hypotenuse.

Accepted Answer

The longer leg is 6 square root 3 units, and the hypotenuse is 12 units. In a 30-60-90 triangle, the side ratio is x to x square root 3 to 2x.

Question 12

A 45-45-90 triangle has legs of length 11 units each. Find the length of the hypotenuse.

Accepted Answer

The hypotenuse is 11 square root 2 units. In a 45-45-90 triangle, the hypotenuse equals a leg times square root 2.

Question 13

In triangle PQR, segment S connects the midpoints of sides PQ and PR. If QR = 24 cm, find the length of midsegment S.

Accepted Answer

The midsegment is 12 cm because a triangle midsegment is parallel to the third side and has half its length.

Question 14

The sides of a triangle are 8, 15, and 17. Determine whether the triangle is acute, right, or obtuse.

Accepted Answer

The triangle is right because 8 squared plus 15 squared equals 64 + 225 = 289, and 17 squared is also 289.

Question 15

Two sides of a triangle are 10 cm and 14 cm. What are the possible integer values for the third side length?

Accepted Answer

The possible integer values are 5 cm through 23 cm. By the triangle inequality, the third side x must be greater than 14 - 10 and less than 14 + 10, so 4 < x < 24.

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Geometry: Triangles (High School)

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