Question

Requesting for a list of rules/properties of triangles and tests of congruents

Answer 1

A triangle is a closed figure made up of three line segments.
Basic properties of triangles

The sum of the angles in a triangle is 180°. This is called the angle-sum property.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

The side opposite to the largest angle is the longest side of the triangle and the side opposite to the smallest angle is the shortest side of the triangle.

An exterior angle of a triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Congruent Triangles

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles. In this lesson, we will consider the four rules to prove triangle congruence. They are called the SSS rule, SAS rule, ASA rule and AAS rule.

Side-Side-Side (SSS) Rule

Side-Side-Side is a rule used to prove whether a given set of triangles are congruent.

The SSS rule states that:

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

Side-Angle-Side (SAS) Rule

Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent.

The SAS rule states that

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

Angle-Side-Angle (ASA) Rule

Angle-side-angle is a rule used to prove whether a given set of triangles are congruent.

The ASA rule states that

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

Angle-Angle-Side (AAS) Rule

Angle-angle-side is a rule used to prove whether a given set of triangles are congruent.

The AAS rule states that

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