What Are The 4 Conditions Of Congruence?


The triangle congruence criteria are:

  • SSS (Side-Side-Side)
  • SAS (Side-Angle-Side)
  • ASA (Angle-Side-Angle)
  • AAS (Angle-Angle-Side)
  • HL (Hypotenuse-Leg, right triangle only)


SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent. ASA (angle-side-angle)

What are the 5 congruence theorems?

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

  • SSS (side, side, side) SSS stands for “side, side, side” and means that we have two triangles with all three sides equal. …
  • SAS (side, angle, side) …
  • ASA (angle, side, angle) …
  • AAS (angle, angle, side) …
  • HL (hypotenuse, leg)

How do you know if it’s AAS or ASA?

ASA stands for “Angle, Side, Angle”, while AAS means “Angle, Angle, Side”. Two figures are congruent if they are of the same shape and size. … ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.

What is congruence rule?

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

Is AAA a congruence condition?

Four shortcuts allow students to know two triangles must be congruent: SSS, SAS, ASA, and AAS. … Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles.

What is AAS congruence rule?

Whereas the Angle-Angle-Side Postulate (AAS) tells us that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

How do you prove AAS?

Angle-side-angle is a rule used to prove 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 non-included side of another triangle, then the triangles are congruent.

Why does AAS congruence not work?

What about SSA (Side Side Angle) theorem? … The ASS Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent.

Does Social Security guarantee congruence?

Given two sides and non-included angle (SSA) is not enough to prove congruence. … You may be tempted to think that given two sides and a non-included angle is enough to prove congruence. But there are two triangles possible that have the same values, so SSA is not sufficient to prove congruence.

What is AAA triangle?

“AAA” means “Angle, Angle, Angle” “AAA” is when we know all three angles of a triangle, but no sides.


What is congruence triangle?

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

How many congruence rules are there?

There are basically four congruency rules that help in checking whether two triangles are congruent and they are SSS, SAS, ASA and RHS.

What is the congruence symbol?

The symbol ≡ means “is congruent to”. Two triangles are similar if they have the same shape. Two similar triangles are equiangular, i.e., angles which correspond are equal.

What are the 3 properties of congruence?

There are three properties of congruence. They are reflexive property, symmetric property and transitive property. All the three properties are applicable to lines, angles and shapes. Reflexive property of congruence means a line segment, or angle or a shape is congruent to itself at all times.

How many types of congruence are there in a triangle?

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).

What is a congruent shape?

Two shapes that are the same size and the same shape are congruent. … They are identical in size and shape.

Is AAA a similar triangle?

Definition: Triangles are similar if the measure of all three interior angles in one triangle are the same as the corresponding angles in the other. This (AAA) is one of the three ways to test that two triangles are similar . … And so, because all three corresponding angles are equal, the triangles are similar.

What do you call the longest side of a right triangle?

The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.

Does SSA prove similarity?

Explain. While two pairs of sides are proportional and one pair of angles are congruent, the angles are not the included angles. This is SSA, which is not a similarity criterion. Therefore, you cannot say for sure that the triangles are similar.

What is SSA similarity theorem?

SSA theorem

Two triangles are similar if the lengths of two corresponding sides are proportional and their corresponding angles across the larger of these two are congruent.

How do you prove similarity?

If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

What are the three similarity theorems?

These three theorems, known as Angle – Angle (AA), Side – Angle – Side (SAS), and Side – Side – Side (SSS), are foolproof methods for determining similarity in triangles.

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