Determine if the Two Triangles Are Congruent. If They Are State How You Know
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Congruent Triangles
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Congruent Triangles
Congruent triangles are triangles that have the same size and shape. This ways that the respective sides are equal and the corresponding angles are equal.
We can tell whether two triangles are coinciding without testing all the sides and all the angles of the 2 triangles. In this lesson, nosotros will consider the four rules to testify triangle congruence. They are called the SSS dominion, SAS rule, ASA rule and AAS rule. In some other lesson, we will consider a proof used for right triangles chosen the Hypotenuse Leg rule. As long every bit one of the rules is truthful, information technology is sufficient to bear witness that the two triangles are congruent.
The following diagrams show the Rules for Triangle Congruency: SSS, SAS, ASA, AAS and RHS. Take notation that SSA is not sufficient for Triangle Congruency. Curl down the page for more than examples, solutions and proofs.
Side-Side-Side (SSS) Rule
Side-Side-Side is a dominion used to prove whether a given set of triangles are coinciding.
The SSS rule states that:
If three sides of one triangle are equal to iii sides of another triangle, then the triangles are coinciding.
In the diagrams beneath, if AB = RP, BC = PQ and CA = QR, then triangle ABC is coinciding to triangle RPQ.
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 some other triangle, and then the triangles are congruent.
An included bending is an angle formed by two given sides.
Included Bending Non-included angle
For the 2 triangles beneath, if AC = PQ, BC = PR and bending C< = bending P, and so by the SAS rule, triangle ABC is congruent to triangle QRP.
Bending-Side-Angle (ASA) Rule
Bending-side-bending is a dominion used to prove whether a given set of triangles are coinciding.
The ASA rule states that:
If two angles and the included side of i triangle are equal to two angles and included side of another triangle, and so the triangles are congruent.
Bending-Angle-Side (AAS) Rule
Bending-side-angle is a rule used to prove whether a given gear up of triangles are congruent.
The AAS rule states that:
If two angles and a non-included side of one triangle are equal to 2 angles and a non-included side of some other triangle, and so the triangles are congruent.
In the diagrams below, if Air conditioning = QP, angle A = bending Q, and angle B = angle R, so triangle ABC is congruent to triangle QRP.
Three Means To Prove Triangles Congruent
A video lesson on SAS, ASA and SSS.
- SSS Postulate: If there exists a correspondence between the vertices of 2 triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.
- SAS Postulate: If there exists a correspondence betwixt the vertices of two triangles such that the two sides and the included bending of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are coinciding.
- ASA Postulate: If there exits a correspondence between the vertices of ii triangles such that two angles and the included side of one triangle are congruent to the respective parts of the other triangle, the two triangles are congruent.
- Show Video Lesson
Using Two Column Proofs To Prove Triangles Congruent
Triangle Congruence by SSS
How to Evidence Triangles Congruent using the Side Side Side Postulate?
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
- Testify Video Lesson
Triangle Congruence by SAS
How to Evidence Triangles Congruent using the SAS Postulate?
If ii sides and the included angle of i triangle are congruent to ii sides and the included angle of another triangle, and then the two triangles are congruent.
- Show Video Lesson
Prove Triangle Congruence with ASA Postulate
How to Prove Triangles Coinciding using the Angle Side Angle Postulate?
If ii angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
- Show Video Lesson
Prove Triangle Congruence past AAS Postulate
How to Bear witness Triangles Congruent using the Angle Angle Side Postulate?
If 2 angles and a non-included side of i triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are coinciding.
- Evidence Video Lesson
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