Triangles - ESSENTIAL POINTS
- 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 ∆ ABC ≅∆
- Criteria for Congruence of triangles:
- (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.
- (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.
- (AAS Congruence Rule): If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.
- (SSS Congruence Rule); If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent.
- (RHS Congruence Rule): If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.
- Angles opposite to equal sides of a triangle are equal.
- Sides opposite to equal angles of a triangle are equal.
- Each angle of an equilateral triangle is of 60°.
- In a triangle, angle opposite to the longer side is larger (greater).
- In a triangle, side opposite to the larger (greater) angle is longer.
- Sum of any two sides of a triangle is greater than the third side.
