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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 12
Given a triangle with sides 7 cm, 24 cm, and 25 cm, prove whether it is a right triangle.
Given that AB is parallel to CD and EF is a transversal, prove that alternate interior angles are equal.
Given that the area of a triangle is 30 cm² and its base is 10 cm, find its height.
Given triangle ABC with AB = AC, and D is the midpoint of BC. Prove that AD bisects angle BAC.
Given a triangle with sides 7 cm, 24 cm, and 25 cm, prove whether it is a right triangle.
Given that AB is parallel to CD and EF is a transversal, prove that alternate interior angles are equal.
Given that the area of a triangle is 30 cm² and its base is 10 cm, find its height.
Given triangle ABC with AB = AC, and D is the midpoint of BC. Prove that AD bisects angle BAC.
Which of the following is a correct statement about the centroid of a triangle? (1) It divides each median in the ratio 1:1 (2) It divides each median in the ratio 2:1 (3) It is always outside the triangle (4) It is the intersection of the altitudes
Which of the following is a necessary condition for two triangles to be similar? (1) All corresponding sides are equal (2) All corresponding angles are equal (3) The triangles are congruent (4) The triangles have equal area
Which of the following is NOT a property of a cyclic quadrilateral? (1) Opposite angles are supplementary (2) All sides are equal (3) It can be inscribed in a circle (4) The sum of opposite angles is 180°
Which of the following is NOT a property of an equilateral triangle? (1) All sides are equal (2) All angles are equal (3) The medians are equal (4) The altitudes are unequal
Fill in the blank: The line segment joining the midpoints of two sides of a triangle is __________ to the third side and half its length.
Fill in the blank: The medians of a triangle intersect at the __________.
Fill in the blank: The perpendicular bisector of a chord passes through the __________ of the circle.
Fill in the blank: The point of intersection of the angle bisectors of a triangle is called the __________.
If two triangles have two angles and the included side equal, are the triangles congruent?
True or False: The angle in a semicircle is always a right angle.
True or False: The circumcenter of a triangle always lies inside the triangle.
True or False: The diagonals of a rectangle are always equal.