what are the methods to prove triangles are congruent

^{Methods of proving triangles are congruent:}

1. Side-Side-Side (SSS) – we have to prove that all three sides are congruent.
2. Side-Angle-Side (SAS) – what’s very important here is that the “Angle” is written between the two sides. ...
3. Angle-Side-Angle (ASA) – just like the “angle” in SAS is in between two sides; the “Side” here should also be in between two angles.
4. Angle-Angle-Side (AAS) – here, the “Side” is not in between two angles. You should not use an Angle-Side-Side (ASS) method or Side-Side-Angle (SSA) method. ...
5. Hypotenuse-Leg (HL) – only used in right triangles.

Full Answer

How do you prove that two triangles are similar?

What are the similarity tests?

• Angle Angle Angle (AAA) If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. …
• Side Angle Side (SAS) …
• Side Side Side (SSS) …
• Right-angle Hypotenuse Side (RHS)

How can you say that triangles are congruent?

What is Triangle Congruence?

• Side – Angle – Side. Side Angle Side (SAS) is a rule used to prove whether a given set of triangles are congruent . ...
• Angle – Angle – Side. The Angle – Angle – Side rule (AAS) states that two triangles are congruent if their corresponding two angles and one non-included side are equal.
• Side – Side – Side. ...
• Angle – Side – Angle. ...

How to prove two triangles have the same centroid?

The important properties of the centroid of a triangle are:

• The centroid of a triangle is located at the intersecting point of all three medians of a triangle
• It is considered one of the three points of concurrency in a triangle, i.e., incenter, circumcenter, centroid
• The centroid is positioned inside a triangle
• At the point of intersection (centroid), each median in a triangle is divided in the ratio of 2: 1

How to find if right triangles are congruent?

With just that one diagonal, we know a tremendous amount about our polygon:

• We created two right triangles, △ GRI △ G R I and △ GN I △ G N I
• We know ∠GRI ≅ ∠GN I ∠ G R I ≅ ∠ G N I (right angles of a rectangle)
• We know ∠N GI ≅ ∠RI G ∠ N G I ≅ ∠ R I G (alternate interior angles of parallel lines intersected by a transversal, the diagonal)
• We know the hypotenuses of both triangles are congruent (GI G I; reflexive property)

How do you prove 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.

What are the 5 theorems that prove triangles congruent?

Thus the five theorems of congruent triangles are SSS, SAS, AAS, HL, and ASA.SSS – side, side, and side. ... SAS – side, angle, and side. ... ASA – angle, side, and angle. ... AAS – angle, angle, and side. ... HL – hypotenuse and leg.

What are the 3 ways to prove triangles similar?

You also can apply the three triangle similarity theorems, known as Angle - Angle (AA), Side - Angle - Side (SAS) or Side - Side - Side (SSS), to determine if two triangles are similar.

Is AAA a way to prove triangles congruent?

Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you're trying to determine if two triangles are congruent, there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them.

What is SSS SAS ASA AAS?

Different rules of congruency are as follows. SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side)

What are the 5 types of congruence?

Two triangles are congruent if they satisfy the 5 conditions of congruence. They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).

Does SSA prove Congruence?

Is SSA a Criterion for Congruence of Triangles? No, the SSA congruence rule is not a valid criterion that proves if two triangles are congruent to each other.

What is AAA similarity theorem?

Euclidean geometry may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

Is aas a similarity theorem?

For the configurations known as angle-angle-side (AAS), angle-side-angle (ASA) or side-angle-angle (SAA), it doesn't matter how big the sides are; the triangles will always be similar. These configurations reduce to the angle-angle AA theorem, which means all three angles are the same and the triangles are similar.

Is aas a congruence theorem?

In geometry, AAS means angle angle side and is one of the congruence theorems among the 5 different theorems that prove the congruency of two triangles.

Is HL a congruence theorem?

The hypotenuse leg theorem is a criterion used to prove whether a given set of right triangles are congruent. The hypotenuse leg (HL) theorem states that; a given set of triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

Side-Side-Side (SSS) Rule

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Side-Angle-Side (SAS) Rule

Angle-Side-Angle (ASA) Rule

Angle-Angle-Side (AAS) Rule

Three Ways to Prove Triangles Congruent

Using Two Column Proofs to Prove Triangles Congruent

SSS

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SAS

Asa

Aas

Hl

Caution! Don't Use "AAA"