Prove Triangle congruence part 1

2 answers:

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ANSWER:

<u>There are five ways to find if two triangles are congruent</u>: SSS, SAS, ASA, AAS and HL.

1. SSS congruency (side, side, side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

For example:–

If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS congruency (side, angle, side)

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

For example:–

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

3. ASA congruency (angle, side, angle)

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

For example:–

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

4. AAS congruency (angle, angle, side)

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.

For example:–

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

5. HL congruency (hypotenuse, leg)

[This one applies only to right angled-triangles]

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

For example:–

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.