Geometry — practice questions with answers
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AB ∥ CD and a transversal cuts AB at E and CD at F. If ∠AEF = (3y − 15)° and ∠EFD = (2y + 25)°,…An exterior angle of a triangle is 110° and one of the interior opposite angles is 45°. What is…A right triangle has legs 6 cm and 8 cm. How far is its centroid from the right-angle vertex?In triangle ABC, AB = 7 cm, AC = 9 cm and BC = 8 cm. Find the length of the median AD.G is the centroid of triangle ABC, whose area is 96 cm². What is the area of triangle BGC?A 25 m ladder rests against a wall with its foot 7 m from the wall. If the top slides down by 4 m,…The hypotenuse of a right triangle is 26 cm and one leg is 14 cm longer than the other. What is…The areas of two similar triangles are in the ratio 16 : 25. What is the ratio of their…A line DE parallel to BC (D on AB, E on AC) divides triangle ABC into two parts of equal area.…Two sides of a triangle are 7 cm and 12 cm. How many integer values are possible for the third side?ABCD is a cyclic quadrilateral. Side AB is produced to E and ∠CBE = 75°. Find ∠ADC.Two circles of radii 10 cm and 17 cm intersect, and their centres are 21 cm apart. What is the…In a circle of radius 10 cm, two parallel chords of lengths 16 cm and 12 cm lie on opposite sides…Two angles form a linear pair and one of them measures 118°. What does the other angle measure?Two complementary angles are in the ratio 4 : 5. What is the larger angle?Two supplementary angles differ by 44°. What is the smaller angle?Lines AB and CD intersect at O. If ∠AOC + ∠BOD = 130°, find ∠BOC.Three straight lines pass through a point O. Going round O, three consecutive angles are x°, 2x°…Two parallel lines are cut by a transversal and one of the eight angles formed is 58°. What is the…In the figure, AB ∥ CD and E is a point between the two lines, to the left of A and C. If ∠BAE =…PQ ∥ RS and a transversal meets PQ at M and RS at N. The bisectors of ∠QMN and ∠MNS meet at T.…AB ∥ CD and a transversal cuts AB at P and CD at Q, with ∠APQ = (5x − 8)° and ∠PQD = (3x + 24)°.…The exterior angle at C of triangle ABC is 128°. If ∠A = ∠B, find ∠A.Angle A of triangle ABC exceeds angle B by 24°, and angle B exceeds angle C by 18°. Find ∠A.In triangle ABC, D is the midpoint of BC and AD = BD. If ∠B = 34°, find ∠C.
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