Angles opposite to equal sides of an isosceles triangle are equal. Given: A isosceles triangle △ ABC in which AB = AC, andangles opposite to equal sides of triangle are ∠B and ∠C. To prove: We need to prove that ∠B and ∠C, are equal ∠B = ∠C. Construction: Draw the bisector […]
Read More →The side opposite to equal angles of a triangle are equal. Given: A triangle △ ABC in which angles opposite to sides AC and AB of are ∠B and ∠C, and ∠B = ∠C. To prove: We need to prove that sides AB and AC, are equal AB = AC. Construction: Draw […]
Read More →If two Lines are parallel to a third line then the lines are parallel to each other. Given: It is given that three lines l, m, and n, and line l ∥ line m and line m ∥ line n. To Prove: Line l ∥ Line n Proof: Let us draw a line p transversal for lines l, m, and n. For lines l […]
Read More →Vertically Opposite Angles Theorem Vertical angles theorem or Vertically opposite angles theorem states that, If two lines intersect each other, then vertically opposite angles are equal. Given: In the above statement, given that two lines intersect each other, so let AB and CD are two lines intersect each other at O as shown in figure so […]
Read More →Angle – Angle – Similarity If two angles of a triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Given: Two △ABC and △PQR such that ∠B = ∠Q, and ∠C = ∠R To prove: △ABC ~ △PQR Proof: In △ABC, ∠A + ∠B +∠C = 1800….(1) by angle sum property In △PQR∠P + […]
Read More →The angle at the centre of a circle is twice the angle at the circumference, when both are subtended by the same arc. Given: A circle with centre at O, arc BC of this circle subtends angles ∠BOC at centre O and ∠BAC at a point A remaining part of the circle. To Proof: ∠BOC […]
Read More →Prove that the angle in a semicircle is a right angle or Angle subtended by a diameter/Semicircle on any circle on any point of circle is 90º. Given: A circle O with centre O. BC is the diameter of circle subtending ∠BAC at […]
Read More →If the diagonals of a Quadrilateral, bisect each other then that Quadrilateral is a Parallelogram Given: ABCD is a quadrilateral with AC and BD are diagonals and diagonals intersect each other at O. i.e. OA = OC and OB = OD To Prove: ABCD is a parallelogram. Proof: In △AOD and △COB […]
Read More →