Equal chords of a circle subtend equal angles at the center. Given: Two equal chords AB and CD of a circle with center O. i,e. AB = CD. To prove: ∠AOB = ∠COD Proof: In △AOB and △ COD OA = OC (Radius of circle)OB = OD (Radius of circle)AB = CD (Given) Hence, △AOB ≅ △ COD (SSS Congruence rule) ∴ ∠AOB […]
Read More →A diagonal of a parallelogram, divides it into two congruent triangles. Given: A parallelogram ABCD and AC is a diagonal, the diagonal AC divides parallelogram ABCD into two triangles △ ABC and △ CDA. To prove: These triangles △ ABD and △CDA are congruent, △ ABC ≅ △ CDA Proof: In △ ABC and △ CDA BC ∥ AD and AC […]
Read More →If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Given: ABCD is a quadrilateral, each pair of opposite sides of quadrilateral ABCD are AB and CD and also sides AD and BC are equal. AB = CD BC = AD To prove: ABCD is a parallelogram. Construction: Join A to C that is AC, is […]
Read More →In a parallelogram opposite sides are equal. Given: A parallelogram ABCD, each pair of Opposite sides of parallelogram are side AB and side DC and side AD and side BC. To prove: Opposite sides of parallelogram are equal that is AB = DC and AD = BC Construction: Join A to C that is AC, is a diagonal, the diagonal AC […]
Read More →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 →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 →What is Theorem in Mathematics In mathematics a theorem is a statement, that has been proved to be true on basis of facts that were already known and used in previously established statements. The process of showing a theorem to be (true) correct is called proof. proofs are an important part of mathematics. […]
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 […]
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