Question

important theoram for math 9th class

Answer 1

HEY MATE ...

Theorem 10.8 of circle chapter is important...

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remainder part of the circle.

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Answer 2

Theorems

Two figures are congruent, if they are of the same shape and of the same size.Two circles of the same radii are congruent.Two squares of the same sides are congruent.If two triangles ABC and PQR are congruent under the correspondence A – P, B-Q and C-R, then symbolically, it is expressed as Δ ABC Δ PQR.

SAS Congruence Rule: If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent. (Axiom: This result cannot be proved with the help of previously known results.)

ASA Congruence Rule: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).

Construction: Two triangles are given as follows in which:
∠ABC=∠DEF∠ABC=∠DEF and ∠ACB=∠DEF∠ACB=∠DEF
Sides AB=DEAB=DE

To prove: ΔABC≅ΔDEFΔABC≅ΔDEF

Proof: ∠ABC=∠DEF∠ABC=∠DEF (given)
AB=DEAB=DE
AC=DFAC=DF
(Sides opposite to corresponding angles are in the same ratio as ratio of angles)
Hence, ΔABC≅ΔDEFΔABC≅ΔDEF (SAS rule)