Question

Given triangles ABC and DEF.

Which triangle congruence theorem can prove triangle ABC congruent to triangle DEF?




Angle-Side-Angle (ASA)

Side-Angle-Side (SAS)

Side-Side-Side (SSS)

All of the above

Answer 1

All of the above.

Explanation:

There are five postulates triangle congruence theorem.

Triangle ABC is said to be congruent with DEF if it satisfies these conditions

1. Side Side Side (SSS) : A triangle ABC is congruent to DEF if the sides AB = DE, BC = EF, and CA = FD. in length. i.e. The three sides of triangle ABC is equal to the three sides of DEF.

2. Side Angle Side (SAS): A triangle ABC is congruent to DEF if the corresponding ANGLE between two equal sides in the triangle are the same. that is SIDE AB = DE and then ANGLE B = angle E and SIDE BC = EF i.e. The equal angle must be in-between two equal corresponding side

3. Angle Side Angle (ASA): A triangle ABC is congruent to DEF if ANGLE A = angle D and SIDE AB = DE and ANGLE B = Angle E. i.e. The equal side must be in-between two equal angles.

4. ANGLE ANGLE SIDE (AAS): A triangle ABC is congruent to DEF if ANGLE A = angle D and ANGLE B = angle E and SIDE BC = EF i.e. The equal sides are after two corresponding angles

The last and not least is called

5. Hypotenuse Leg (HL): This is used for right angled triangles, and it states that A triangle ABC is congruent to DEF if the HYPOTENUSE AC = DF and ANY OF THE LEGS (AB or BC) is equal to the legs DE or EF. i.e. A leg and the hypotenuse of a right angled triangle are equal

Answer 2

All of the above

Explanation:

• SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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

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