Practice high school triangle skills including angle relationships, congruence, similarity, the Pythagorean Theorem, area, and special right triangles.
Read each problem carefully. Show your work in the space provided. Use correct units when needed.
Classifying triangles, proving congruence, and solving for missing measures
Geometry - Grade 9-12
- 1
In triangle ABC, angle A measures 42 degrees and angle B measures 68 degrees. Find the measure of angle C.
- 2
A triangle has side lengths 7 cm, 10 cm, and 15 cm. Determine whether these lengths can form a triangle. Explain your reasoning.
- 3
Classify a triangle with side lengths 9, 9, and 14 by its sides and by its angles.
- 4
In triangle DEF, DE is congruent to DF. If angle E measures 54 degrees, find the measures of angles D and F.
- 5
Two triangles have side lengths 6, 8, 10 and 9, 12, 15. Are the triangles similar? Explain.
- 6
A right triangle has legs of length 12 inches and 16 inches. Find the length of the hypotenuse.
- 7
A right triangle has a hypotenuse of 13 meters and one leg of 5 meters. Find the length of the other leg.
- 8
Find the area of a triangle with a base of 18 cm and a height of 7 cm.
- 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?
- 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.
- 11
A 30-60-90 triangle has a shorter leg of 6 units. Find the longer leg and the hypotenuse.
- 12
A 45-45-90 triangle has legs of length 11 units each. Find the length of the hypotenuse.
- 13
In triangle PQR, segment S connects the midpoints of sides PQ and PR. If QR = 24 cm, find the length of midsegment S.
- 14
The sides of a triangle are 8, 15, and 17. Determine whether the triangle is acute, right, or obtuse.
- 15
Two sides of a triangle are 10 cm and 14 cm. What are the possible integer values for the third side length?