Congruent Triangles Worksheet Answer Key

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent. Congruent triangles make up the triangles in Figure 1.

Triangle congruence

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle’s size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements. Let’s go over them in more depth.

Triangle Conditions of Congruence

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

SSS Congruence Criteria

Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their corresponding sides and included angles are the same on each side of each other.

ASA Congruence Criteria

Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and corresponding angles are equal in size to those of the other triangle.

AAS Congruence Criteria

Angle-Angle-Side criterion is also known as the AAS criterion. Two triangles are said to be congruent according to the AAS criterion if any two angles and the non-included side of one triangle match the corresponding angles and side of the other triangle.

RHS Congruence Criteria

Right angle-hypotenuse-side congruence is referred to as the RHS criterion. If the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, then two triangles are said to be congruent according to this criterion.

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Significant notes

• When one triangle’s six components—its three sides and three angles—are equal to the corresponding six components of the other triangle, the two triangles are said to be congruent.
• To establish whether two triangles are congruent, there are five requirements. The criteria are SSS, SAS, ASA, AAS, and RHS.
• Due to the possibility that one triangle is an expanded replica of the other, two triangles with equal corresponding angles may not be congruent to one another. As a result, there is no AAA congruence criteria.
• We use the symbol () to denote congruency.
• Two triangles’ areas and perimeters are equal if they are congruent.

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