How Do You Know When a Triangle Is Congruent
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Congruent Triangles
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Coinciding Triangles
Congruent triangles are triangles that take the aforementioned size and shape. This ways that the corresponding sides are equal and the corresponding angles are equal.
Nosotros can tell whether two triangles are congruent without testing all the sides and all the angles of the ii triangles. In this lesson, nosotros volition consider the iv rules to prove triangle congruence. They are called the SSS rule, SAS dominion, ASA dominion and AAS rule. In some other lesson, we will consider a proof used for correct triangles called the Hypotenuse Leg rule. As long as one of the rules is truthful, it is sufficient to prove that the 2 triangles are congruent.
The following diagrams bear witness the Rules for Triangle Congruency: SSS, SAS, ASA, AAS and RHS. Take note that SSA is not sufficient for Triangle Congruency. Scroll down the page for more examples, solutions and proofs.
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 3 sides of one triangle are equal to three sides of another triangle, so the triangles are congruent.
In the diagrams below, if AB = RP, BC = PQ and CA = QR, then triangle ABC is congruent to triangle RPQ.
Side-Angle-Side (SAS) Rule
Side-Angle-Side is a rule used to prove whether a given set up of triangles are congruent.
The SAS rule states that:
If two sides and the included bending of 1 triangle are equal to ii sides and included bending of another triangle, then the triangles are congruent.
An included bending is an bending formed by two given sides.
Included Angle Not-included angle
For the ii triangles beneath, if AC = PQ, BC = PR and angle C< = bending P, then by the SAS rule, triangle ABC is congruent to triangle QRP.
Bending-Side-Angle (ASA) Rule
Angle-side-angle is a rule used to prove whether a given gear up of triangles are congruent.
The ASA rule states that:
If 2 angles and the included side of one triangle are equal to two angles and included side of another triangle, and so the triangles are congruent.
Angle-Angle-Side (AAS) Rule
Angle-side-angle is a dominion used to show 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 not-included side of some other triangle, then the triangles are congruent.
In the diagrams below, if Air conditioning = QP, angle A = angle Q, and angle B = angle R, so triangle ABC is congruent to triangle QRP.
Three Ways To Prove Triangles Congruent
A video lesson on SAS, ASA and SSS.
- SSS Postulate: If there exists a correspondence betwixt the vertices of two triangles such that three sides of one 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 2 triangles such that the two sides and the included angle of 1 triangle are congruent to the respective parts of the other triangle, the two triangles are congruent.
- ASA Postulate: If in that location exits a correspondence between the vertices of two 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 congruent.
- Show Video Lesson
Using 2 Cavalcade Proofs To Prove Triangles Coinciding
Triangle Congruence by SSS
How to Bear witness Triangles Congruent using the Side Side Side Postulate?
If 3 sides of one triangle are congruent to three sides of another triangle, then the two triangles are coinciding.
- Show Video Lesson
Triangle Congruence by SAS
How to Prove 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 2 triangles are congruent.
- Show Video Lesson
Prove Triangle Congruence with ASA Postulate
How to Evidence Triangles Coinciding using the Angle Side Angle Postulate?
If two angles and the included side of 1 triangle are coinciding to two angles and the included side of another triangle, then the ii triangles are coinciding.
- Evidence Video Lesson
Prove Triangle Congruence by AAS Postulate
How to Prove Triangles Congruent using the Angle Angle Side Postulate?
If two angles and a non-included side of one triangle are congruent to ii angles and a non-included side of another triangle, then the ii triangles are congruent.
- Show Video Lesson
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