Geometry — practice questions, page 2
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Triangle ABC is isosceles with AB = AC and ∠BAC = 40°. BD is the perpendicular from B to AC. Find…The internal bisectors of ∠B and ∠C of triangle ABC meet at O, and ∠BOC is three times ∠A. Find ∠A.In triangle ABC, ∠B = 64° and ∠C = 36°. The internal bisector of ∠B meets the bisector of the…For a triangle ABC with ∠B = 2∠C, the bisector of ∠A meets BC at D and ∠ADC = 100°. Find ∠C.The angles of a triangle are (x + 15)°, (2x − 5)° and (3x + 20)°. What is the smallest angle?The exterior angles of a triangle are in the ratio 4 : 5 : 6. What is the largest interior angle?The angles of a triangle are in arithmetic progression and the largest angle is twice the…Triangle ABC has AB = AC, and a point D on AC satisfies AD = BD = BC. Find ∠BAC.A line through vertex A of triangle ABC is drawn parallel to BC. It makes angles of 52° with AB…In triangle ABC, ∠A : ∠B = 2 : 3 and ∠C exceeds ∠A by 40°. The bisector of ∠C meets AB at D. Find…A triangle has sides 10 cm, 14 cm and 18 cm. Find the perimeter of the triangle formed by joining…Corresponding sides of two similar triangles are 6 cm and 9 cm. The smaller triangle has an area…At a certain time of day, a boy 1.8 m tall casts a shadow 2.4 m long. At the same moment a flag…ABC is a right triangle with ∠B = 90°, AB = 15 cm and BC = 20 cm. BD is drawn perpendicular to AC.…In triangle PQR, ∠Q = 90° and QS is perpendicular to PR. If PS = 3.6 cm and SR = 6.4 cm, find PQ.A triangle has sides 8 cm, 15 cm and 16 cm. What kind of triangle is it?Two sides of a triangle are 7 cm and 10 cm, and the third side, x cm, is the longest side. For how…The medians AD and BE of triangle ABC meet at G. If GD = 3.5 cm, what is the length of AD?In triangle ABC, ∠A = 90°, AB = 6 cm and AC = 8 cm. How long is the median drawn from B?The sides of triangle ABC are AB = 13 cm, AC = 15 cm and BC = 14 cm. Find the length of the median…The sides of a triangle are 10 cm, 17 cm and 21 cm. What is the altitude drawn to the longest side?In triangle PQR, PS bisects ∠P and meets QR at S. If PQ = 9 cm, PR = 6 cm and QR = 10 cm, find QS.The bisector of the exterior angle at A of triangle ABC meets BC produced at E. If AB = 10 cm, AC…Which of these sets of lengths can NOT be the sides of a triangle?How many different triangles with whole-number side lengths (in cm) have a perimeter of 15 cm?
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