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.

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.

Given that triangle ABC is congruent to triangle DEF, which of the following must be true? (1) AB = DE (2) ∠A = ∠D (3) BC = EF (4) All of the above

Which congruence criterion is NOT valid for triangles? (1) SSS (2) SAS (3) ASA (4) SSA

Which of the following is a property of the centroid of a triangle? (1) It divides each median in the ratio 2:1 (2) It is the center of the circumscribed circle (3) It is always outside the triangle (4) It is the intersection of the angle bisectors

Which of the following is a valid method to prove that two triangles are congruent? (1) SSS (Side-Side-Side) (2) AAA (Angle-Angle-Angle) (3) SAS (Side-Angle-Side) (4) SSA (Side-Side-Angle)

Fill in the blank: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are ________.

Fill in the blank: In a parallelogram, opposite sides are ________ and ________.

Fill in the blank: The diagonals of a square are ________ and bisect each other at right angles.

Fill in the blank: The midpoint of the hypotenuse of a right triangle is ________ from all three vertices.

True or False: If two triangles have equal corresponding angles, they are always congruent.

True or False: The angle bisectors of a triangle always meet at a single point.

True or False: The diagonals of a kite are always perpendicular to each other.

True or False: The diagonals of a parallelogram always bisect each other.