ANGLE SIDE ANGLE Congruence Postulate

About "ANGLE SIDE ANGLE Congruence Postulate"

ANGLE SIDE ANGLE Congruence Postulate (ASA) :

ASA or Angle-Side-Angle Congruence postulate is a rule which can be used to prove the congruence of two triangles. 

Angle Side Angle Congruence Postulate

Explanation :

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

ANGLE SIDE ANGLE Congruence Postulate - Examples

Example 1 :

In the diagram given below, prove that ΔABD  ≅  ΔEBC using two column proof

Solution :

Statements

BD  ≅  BC

AD || EC

∠D  ≅  ∠C

∠ABD  ≅  ∠EBC

ΔABD  ≅  ΔEBC

Reasons

Given

Given

Alternate Interior Angles Theorem

Vertical Angles Theorem

ASA Congruence Postulate

Example 2 :

Check whether two triangles PQR and CDE are congruent.

Solution :

(i) ∠R  =  ∠D (Given)

(ii) PR  =  ED (Given)

(iii) ∠P  =  ∠E (Given)

Hence, the two triangles PQR and CDE are congruent by ASA postulate. 

Other Triangle Congruence Postulates and Theorems

1. Side-Side-Side (SSS) Congruence Postulate

If three sides of one triangle is congruent to three sides of another triangle, then the two triangles are congruent.

2. Side-Angle-Side (SAS) Congruence Postulate

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

3. Angle-Angle-Side (AAS) Congruence Postulate

If two angles and non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

4. Hypotenuse-Leg (HL) Theorem

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

5. Leg-Acute (LA) Angle Theorem

If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.

6. Hypotenuse-Acute (HA) Angle Theorem

If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

7. Leg-Leg (LL) Theorem

If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.

Apart from the problems given above, if you need more problems on triangle congruence postulates,

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