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Congruence of Triangles Class 9 similarly

Triangle

A closed figure formed by three intersecting lines is called a triangle. A triangle has three sides, three angles and three vertices.

Congruent figures

Congruent means equal in all respects or figures whose shapes and sizes are both the same for example, two circles of the same radii are congruent. Also two squares of the same sides are congruent.

Congruent Triangles

two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly.

• If two triangles ABC and PQR are congruent under the correspondence P,B Q and then symbolically, it is expressed as

$Congruent Triangles$

• In congruent triangles corresponding parts are equal and we write ’CPCT’ for corresponding parts of congruent triangles.

SAS congruency rule

Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
For example as shown in the figure satisfy SAS congruent criterion.

$SAS congruency rul$

ASA Congruence Rule -

Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.
. For examples shown below satisfy ASA congruence criterion.

$ASA Congruence Rule$

AAS Congruence Rule

Two triangle are congruent if any two pairs of angles and one pair of corresponding sides are equal
for example shown below satisfy AAS congruence criterion.

$AAS Congruence Rule$

• AAS criterion for congruence of triangles is a particular case of ASA criterion.

Isosceles Triangle

A triangle in which two sides are equal is called an isosceles triangle. For example shown below is an isosceles triangle with AB=AC.

$Isosceles Triangle - A triangle$

• Angle 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 60^o .

SSS congruence Rule

If three sides of one triangle are equal to the three sides of another triangle then the two triangles are congruent.
For example as shown in the figure satisfy SSS congruence criterion

$SSS congruence Rule$

RHS Congruence Rule

- If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle then the two triangle are congruent.
For example shown below satisfy RHS congruence criterion.