Question

What are the postulates for congruent triangles

Answer 1

Hi there!

There are 5 ways to find if two triangles are congruent :

SSS, SAS, ASA, AAS & HL

1. SSS (Side, Side, Side)

Means that we have two triangles with 3 sides equal.

⇒ If 3 sides of one triangle are equal to 3 sides of another triangle, the triangles are congruent.

2. SAS (Side, Angle, Side)

Means that we have two triangles where we know 2 sides and the included angle are equal.

⇒ If 2 sides and the includent angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA (Angle, Side, Angle)

Means that we have two triangles where we know 2 angles and the included side are equal.

⇒ If 2 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 (Angle, Angle, Side)

Means thant we have two triangles where we know 2 angles and the non-included side are equal.

⇒ If 2 angles and the non-included side of one triangle are equal to the coresponding angles and side of another triangle, the triangles are congruent.

5. HL (Hypotenuse, leg)

** This one only applies to right-angled triangles.**

Hypotenuse: The longest side of a right-angled triangle.

Legs: The other 2 sides of the right-angled triangle.

Means we have two right-angled triangles with the same length of hypotenuse and the same length for one of the other 2 legs (it doesn't matter which leg since the triangles could be rotated).

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

There you go! I really hope this helped, if there's anything just let me know! :)