Geometric Proofs

Math ⇒ Geometry

Geometric Proofs starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Geometric Proofs. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 10

Explain why the diagonals of a rhombus bisect each other at right angles.

Explain why the sum of the angles in a triangle is always 180 degrees.

Explain why the sum of the exterior angles of any polygon is always 360 degrees.

Explain why vertical angles are always equal.

Given: In triangle ABC, AB = AC. Prove that ∠B = ∠C.

If the measure of one angle of a triangle is 90°, and the other two angles are equal, what is the measure of each of the other two angles?

If the sides of a triangle are 5 cm, 12 cm, and 13 cm, prove that it is a right triangle.

If the sum of two angles of a triangle is 120°, what is the measure of the third angle?

If two chords of a circle are equal, what can you say about their distances from the center?

If two sides of a triangle are equal, what can you say about the angles opposite those sides?

If two triangles have sides in the ratio 2:3, are the triangles necessarily similar?

Prove that the base angles of an isosceles triangle are equal.

Prove that the diagonals of a rectangle are equal in length.

Prove that the sum of the interior angles of a quadrilateral is 360 degrees.

State the converse of the Pythagorean Theorem.

Given: In triangle ABC, D and E are points on AB and AC respectively such that DE is parallel to BC. Prove that AD/DB = AE/EC.

Given: In triangle PQR, the angle bisector of ∠P meets QR at point D. If QD = 4 cm, DR = 6 cm, and PQ = 5 cm, use the Angle Bisector Theorem to find the length of PR.

In triangle XYZ, XY = XZ and M is the midpoint of YZ. Prove that XM is perpendicular to YZ.

Prove that if two lines are parallel and a transversal cuts them, then the sum of the interior angles on the same side of the transversal is 180 degrees.

Prove that the opposite angles of a parallelogram are equal.