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### Congruent Triangles

Congruent triangles room triangles that have the same size and shape. This method that the equivalent sides room equal and also the equivalent angles are equal.

You are watching: What else must you know to prove the triangles congruent by sas

We have the right to tell whether 2 triangles are congruent without trial and error all the sides and also all the angle of the 2 triangles. In this lesson, we will consider the 4 rules come prove triangle congruence. Lock are referred to as the **SSS** rule, **SAS** rule, **ASA** rule and also **AAS** rule. In an additional lesson, we will take into consideration a proof supplied for appropriate triangles called the Hypotenuse foot rule. As long as one of the rule is true, that is enough to prove the the 2 triangles space congruent.

The complying with diagrams present the Rules for Triangle Congruency: SSS, SAS, ASA, AAS and RHS. Take note that SSA is not enough for Triangle Congruency. Scroll down the page for much more examples, solutions and also proofs.

Side-Side-Side (SSS) Rule

**Side-Side-Side** is a dominion used to prove even if it is a given set of triangles space congruent.

The **SSS** dominance states that:If **three sides** that one triangle room equal come **three sides** of an additional triangle, climate the triangles room congruent.

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

**Side-Angle-Side** is a preeminence used come prove even if it is a given collection of triangles room congruent.

The **SAS** dominance states that:If **two sides and also the contained angle** the one triangle are equal to **two sides and included angle** of one more triangle, climate the triangles are congruent.

An **included angle** is one angle created by two given sides.

For the 2 triangles below, if *AC* = *PQ*, *BC* = *PR* and angle *CAngle-Side-Angle (ASA) Rule*

**Angle-side-angle** is a preeminence used come prove even if it is a given collection of triangles are congruent.

*The ASA dominion states that:If two angles and also the included side the one triangle space equal come two angles and included side of another triangle, climate the triangles room congruent.*

*Angle-Angle-Side (AAS) Rule*

**Angle-side-angle** is a preeminence used to prove even if it is a given set of triangles room congruent.

The **AAS** preeminence states that:If **two angles and also a non-included side** the one triangle are equal come **two angles and a non-included side** of an additional triangle, climate the triangles room congruent.

In the diagrams below, if *AC* = *QP*, edge *A* = edge *Q*, and also angle *B* = angle *R*, climate triangle *ABC* is congruent to triangle *QRP*.

A video clip lesson on SAS, ASA and SSS.

**SSS Postulate:**If there exists a correspondence in between the vertices of 2 triangles together that three sides of one triangle room congruent to the matching sides of the other triangle, the two triangles space congruent.**SAS Postulate:**If over there exists a correspondence in between the vertices of two triangles such the the 2 sides and also the included angle that one triangle room congruent come the corresponding parts the the various other triangle, the two triangles room congruent.**ASA Postulate:**If there exits a correspondence in between the vertices of two triangles such that two angles and the consisted of side that one triangle room congruent come the corresponding parts of the various other triangle, the two triangles room congruent. utilizing Two tower Proofs to Prove triangles Congruent**Triangle Congruence through SSS** exactly how to Prove triangles Congruent making use of the side Side side Postulate? If three sides that one triangle are congruent to three sides of an additional triangle, then the 2 triangles space congruent.

**Triangle Congruence through SAS** how to Prove triangle Congruent utilizing the SAS Postulate? If two sides and the included angle of one triangle room congruent to 2 sides and also the consisted of angle of an additional triangle, climate the 2 triangles are congruent.

**Prove Triangle Congruence with ASA Postulate** how to Prove triangle Congruent using the Angle next Angle Postulate? If 2 angles and also the consisted of side of one triangle are congruent to 2 angles and also the had side of an additional triangle, then the two triangles room congruent.

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**Prove Triangle Congruence through AAS Postulate** exactly how to Prove triangles Congruent utilizing the angle Angle next Postulate? If 2 angles and a non-included side of one triangle room congruent to 2 angles and a non-included next of another triangle, climate the 2 triangles space congruent.

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