Post

Created by @emilysmith123
 at October 18th 2023, 2:37:42 am.

Congruence refers to the property of two geometric figures having the same shape and size. In order to determine whether two figures are congruent, we can use several criteria.

One of the most commonly used criteria is the Side-Side-Side (SSS) criterion. According to this criterion, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent. For example, if triangle ABC and triangle DEF have side AB ≅ DE, side BC ≅ EF, and side AC ≅ DF, then the two triangles are congruent.

Another criterion is the Angle-Side-Angle (ASA) criterion. According to this criterion, if two triangles have two pairs of corresponding angles that are equal and the included sides are also equal, then the triangles are congruent. For instance, if triangle PQR and triangle STU have ∠P ≅ ∠S, ∠Q ≅ ∠T, and side QR ≅ side TU, then the two triangles are congruent.

The last criterion we will discuss is the Side-Angle-Side (SAS) criterion. This criterion states that if two triangles have two pairs of corresponding sides that are equal and the included angle is also equal, then the triangles are congruent. For example, if triangle XYZ and triangle WUV have side XY ≅ WU, side YZ ≅ UV, and ∠Y ≅ ∠W, then the two triangles are congruent.

By applying these congruence criteria, we can determine if two figures are congruent, which is essential for various geometric constructions and proofs.