Asa And Aas Triangle Congruence

Congruent Triangles

Congruent Triangles
Rules for Triangle Congruency	SSS Rule	SAS Rule
ASA Rule	AAS Dominion	Two-column Proofs

Rules for Triangle Congruency

Congruent triangles are triangles that take the same size and shape. This ways that the corresponding sides are equal and the corresponding angles are equal.

We can tell whether ii 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 dominion.
In another lesson, we will consider a proof used for right triangles called the Hypotenuse Leg rule. Equally long as one of the rules is true, it is sufficient to testify that the two triangles are congruent.

The post-obit diagrams show the Rules for Triangle Congruency: SSS, SAS, ASA, AAS and RHS. Accept note that SSA is not sufficient for Triangle Congruency. Scroll down the page for more examples, solutions and proofs.

Rules for Congruent Triangles

Side-Side-Side (SSS) Rule

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

The SSS rule states that:
If iii sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

In the diagrams below, if AB = RP, BC = PQ and CA = QR, then triangle ABC is congruent to triangle RPQ.

sss rule

Side-Angle-Side (SAS) Rule

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

The SAS rule states that:
If two sides and the included bending of one triangle are equal to two sides and included bending of another triangle, and so the triangles are congruent.

An included angle is an angle formed by 2 given sides.

Included Bending Non-included angle

For the two triangles below, if AC = PQ, BC = PR and angle C< = bending P, then by the SAS rule, triangle ABC is coinciding to triangle QRP.

congruent triangles

Angle-Side-Angle (ASA) Rule

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

The ASA rule states that:
If two angles and the included side of one triangle are equal to ii angles and included side of another triangle, then the triangles are congruent.

Bending-Angle-Side (AAS) Rule

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

The AAS rule states that:
If 2 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 coinciding.

In the diagrams below, if AC = QP, bending A = angle Q, and angle B = bending R, then triangle ABC is congruent to triangle QRP.

Three Means To Evidence Triangles Congruent

A video lesson on SAS, ASA and SSS.

SSS Postulate: If at that place exists a correspondence between the vertices of two triangles such that three sides of ane triangle are coinciding to the corresponding sides of the other triangle, the two triangles are congruent.
SAS Postulate: If there exists a correspondence between the vertices of ii triangles such that the two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the ii triangles are congruent.
ASA Postulate: If there exits a correspondence betwixt the vertices of ii triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are coinciding.

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Using Two Cavalcade Proofs To Testify Triangles Coinciding

Triangle Congruence past SSS
How to Prove Triangles Coinciding using the Side Side Side Postulate?
If three sides of one triangle are coinciding to iii sides of some other triangle, then the two triangles are congruent.

Show Video Lesson

Triangle Congruence past SAS
How to Show Triangles Congruent using the SAS Postulate?
If two sides and the included bending of one triangle are congruent to two sides and the included angle of another triangle, then the ii triangles are congruent.

Evidence Video Lesson

Prove Triangle Congruence with ASA Postulate
How to Evidence Triangles Congruent using the Bending Side Angle Postulate?
If two angles and the included side of one triangle are congruent to two angles and the included side of some other triangle, and then the 2 triangles are congruent.

Prove Video Lesson

Prove Triangle Congruence by AAS Postulate
How to Prove Triangles Congruent using the Angle Angle Side Postulate?
If 2 angles and a not-included side of one triangle are congruent to ii angles and a non-included side of another triangle, then the ii triangles are congruent.

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