ANGLE SIDE ANGLE Congruence Postulate

What is the SAS Condition for Congruence? | Don’t Memorise
What is the SAS Condition for Congruence? | Don’t Memorise

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

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.

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.

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.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Aug 25, 23 12:39 PM

Aug 24, 23 11:03 PM

Aug 23, 23 06:32 AM

You are watching: ANGLE SIDE ANGLE Congruence Postulate. Info created by THVinhTuy selection and synthesis along with other related topics.

Rate this post

Related Posts