Question Bank: Triangles

Define similarity of triangles and explain the criteria for similarity.

If two triangles have equal corresponding angles, are they always similar? Justify your answer.

Prove that if two triangles have their corresponding sides in the same ratio, then they are similar.

In a triangle ABC, if angle A = 50 degrees and angle B = 70 degrees, find the measure of angle C.

In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, determine if the triangle is a right-angled triangle.

Prove that the sum of the angles of a triangle is always 180 degrees.

In triangle XYZ, if angle X = 60 degrees and angle Y = 70 degrees, find the measure of angle Z.

If two triangles are similar, what can you say about the lengths of their corresponding sides?

In triangle ABC, if AB = 5 cm, BC = 7 cm, and AC = 8 cm, determine if the triangle is a scalene triangle.

Prove that if two triangles have equal corresponding angles, then their corresponding sides are in the same ratio.

In triangle LMN, if angle L = 90 degrees and angle M = 45 degrees, find the measure of angle N.

If two triangles have their corresponding sides in the ratio 3:4, and one of the angles is 60 degrees, find the measure of the corresponding angle in the other triangle.

In triangle PQR, if PQ = 4 cm, QR = 6 cm, and PR = 8 cm, determine if the triangle is an equilateral triangle.

Prove that if two triangles have equal corresponding angles, then they are similar.

If two triangles are similar, what can you say about the measures of their corresponding angles?

In triangle ABC, if AB = 3 cm, BC = 4 cm, and AC = 5 cm, determine if the triangle is a right-angled triangle.

Prove that if two triangles have their corresponding sides in the same ratio, then their corresponding angles are equal.

In triangle LMN, if angle L = 60 degrees and angle M = 70 degrees, find the measure of angle N.

If two triangles have equal corresponding angles, are their corresponding sides always in the same ratio? Justify your answer.

In triangle PQR, if PQ = 7 cm, QR = 9 cm, and PR = 12 cm, determine if the triangle is an isosceles triangle.

Prove that if two triangles have equal corresponding angles, then their corresponding sides are in the same ratio.

In triangle XYZ, if angle X = 80 degrees and angle Y = 60 degrees, find the measure of angle Z.

If two triangles are similar, what can you say about the lengths of their corresponding sides?

In triangle ABC, if AB = 6 cm, BC = 8 cm, and AC = 10 cm, determine if the triangle is a scalene triangle.

Define similarity of triangles and explain the criteria for similarity.

If two triangles have corresponding angles of 30°, 60°, and 90°, are they similar? Justify your answer.

In a triangle ABC, if angle A = 50° and angle B = 70°, find the measure of angle C.

Prove that two triangles are similar if their corresponding angles are equal.

In a triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, is the triangle a right-angled triangle?

If two triangles have sides in the ratio 3:4, 6:8, and 9:12, are they similar? Explain.

Prove that the mid-segment of a triangle is parallel to the third side.

In a triangle XYZ, if angle X = 90° and angle Y = 45°, find the measure of angle Z.

If two triangles have sides in the ratio 5:7, 10:14, and 15:21, are they similar? Justify your answer.

Prove that the line joining the midpoints of two sides of a triangle is parallel to the third side.

In a triangle ABC, if AB = 5 cm, BC = 7 cm, and AC = 8 cm, find the measure of angle A.

If two triangles have angles of 40°, 60°, and 80°, are they similar? Explain.

Prove that the diagonals of a quadrilateral bisect each other if the quadrilateral is a trapezium.

In a triangle LMN, if angle L = 70° and angle M = 50°, find the measure of angle N.

If two triangles have sides in the ratio 2:3, 4:6, and 6:9, are they similar? Justify your answer.

Prove that the line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

In a triangle PQR, if PQ = 9 cm, QR = 12 cm, and PR = 15 cm, find the measure of angle Q.

If two triangles have angles of 50°, 70°, and 60°, are they similar? Explain.

Prove that the line joining the midpoints of any two sides of a triangle is parallel to the third side.

If two triangles have sides in the ratio 4:5, 8:10, and 12:15, are they similar? Justify your answer.

Prove that the diagonals of a quadrilateral intersect at right angles if the quadrilateral is a rectangle.

In a triangle UVW, if angle U = 100° and angle V = 40°, find the measure of angle W.

If two triangles have angles of 30°, 45°, and 105°, are they similar? Explain.

Prove that the line joining the midpoints of the diagonals of a quadrilateral is parallel to the fourth side if the quadrilateral is a parallelogram.

Define similarity of triangles and explain the criteria for similarity.

If two triangles have angles of measure 30°, 60°, and 90°, are they similar? Justify your answer.

In a triangle ABC, if angle A = 50° and angle B = 70°, find the measure of angle C.

Prove that if two triangles have their corresponding angles equal, then they are similar.

In a triangle PQR, if PQ = 5 cm, QR = 7 cm, and PR = 8 cm, is it a right-angled triangle? Justify your answer.

If two triangles have sides in the ratio 3:4, are they similar? Explain.

Prove that the sum of the angles of a triangle is 180°.

In a triangle XYZ, if angle X = 90° and angle Y = 45°, find the measure of angle Z.

If two triangles have sides in the ratio 2:3, are they similar? Justify your answer.

Prove that if two triangles have their corresponding sides in the same ratio, then they are similar.

In a triangle ABC, if AB = 6 cm, BC = 8 cm, and AC = 10 cm, is it a right-angled triangle? Justify your answer.

Prove that the altitude drawn from the vertex of the right angle of a right-angled triangle to its hypotenuse divides the triangle into two similar triangles.

In a triangle LMN, if angle L = 40° and angle M = 60°, find the measure of angle N.

If two triangles have angles of measure 45°, 45°, and 90°, are they similar? Justify your answer.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

In a triangle PQR, if PQ = 4 cm, QR = 6 cm, and PR = 8 cm, is it a right-angled triangle? Justify your answer.

If two triangles have sides in the ratio 5:7, are they similar? Explain.

Prove that the medians of a triangle intersect at a point that divides each median in the ratio 2:1.

In a triangle UVW, if angle U = 80° and angle V = 50°, find the measure of angle W.

If two triangles have sides in the ratio 3:5, are they similar? Justify your answer.

Prove that the bisectors of the angles of a triangle intersect at a point called the incenter.

In a triangle XYZ, if XZ = 9 cm, YZ = 12 cm, and XY = 15 cm, is it a right-angled triangle? Justify your answer.

If two triangles have angles of measure 60°, 60°, and 60°, are they similar? Explain.

Prove that the circumcenter of a triangle is the point of intersection of the perpendicular bisectors of its sides.

In a triangle RST, if angle R = 70° and angle S = 50°, find the measure of angle T.