WHAT IS A CONGRUENT TRIANGLE??

Definition

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

What makes a triangle?

A triangle is composed of 6 parts:3 sides3 angles

If all 6 of these parts are congruent to another triangle, then we can say that the two triangles are congruent.

Visual/Picture

Order Matters!!

It is very important to remember that the order of the congruent parts of triangles matters.

Examples/Models

Non-Examples

Congruent Triangle

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

Triangle Congruence

SAS, AAS, ASA, SSS, HL

Shortcuts to congruence

Should we really need to find all 6 parts of a triangle to show they are congruent or can we use shortcuts?

Side-Side-Side

If two triangles have ALL 3 of the same side lengths, then we can say they are congruent by the SSS postulate

side

side

side

Side-Angle-Side

If two triangles have the same side lengths and the same angle measure in-between those sides, the two triangles are congruent by the SAS postulate.

side

angle side

Angle-Side-Angle

If two triangles have 2 congruent angles and a congruent side in-between those angles, then they are congruent by the ASA postulate

angleangle

side

Angle-Angle-Side

If two triangles have 2 congruent angles and a congruent side that isn’t in-between them, then the triangles are congruent by the AAS postulate

angle

angle

side

What about Angle-Side-Side? Angle-Side-Side is not enough to

prove triangles are congruent. As an easy way to remember

that:

don’t be an and try to useA.S.S.

Hypotenuse-Leg

If the hypotenuse and the same leg of two right triangles are congruent then the two right triangles are congruent.

hypot hypotleg leg