The common relation between geometric figures is congruency. The shapes or figures are congruent if the length of the sides and angles measure the same.

**Triangle Congruence
**Congruent triangles are triangles that have equal lengths of sides and angles. Each pair of the corresponding vertices, sides and angles measure the same.

If all the corresponding angles, for example, ∠A = ∠D, ∠E = ∠B, and ∠C = ∠F are congruent and all of the corresponding sides like lines a = d, b = e and c = d have the same measure, then the two triangles are congruent.

If in a given triangle not all the sides and angles are given, it can still be congruent. The congruent triangles must satisfy at least one of these conditions:

a. If the three sides of a triangle are congruent to the other three sides of another triangle, then the triangle is congruent. In the given two triangles with a given of only the measure of its three sides, if all sides are congruent, then the angles are also congruent. It is called “__SSS__“, meaning the three sides are congruent.

Example:

Given the measures of a triangle, which is 5, 15 and 20 cm, and the measures of the sides of the other triangle are the same, then the two triangles are congruent.

b. If an angle between the given two sides is congruent, then the two triangles are also congruent. When the triangles have two congruent sides and the included angle of one triangle is congruent, then the two triangles are congruent. It is “__SAS__” or sides, included angle and another side are congruent.

Example:

Using SAS, the two triangles corresponding sides and the angle in between the two sides measures the same. The length of the sides measures 5cm, the included angle is a right angle of a 90-degree angle and 15 cm is the length of other sides. Since the conditions are satisfied, they are congruent.

c. If the two angles and one side of a triangle is congruent, then the two triangles are congruent. This condition will work even when the side is between the triangle or non included sides. It is when __ASA __or an angle, side and angle are congruent in two triangles that make them congruent triangles.

Example:

A 90-degree angle, 5 cm sides and 60-degree angle that measure the same as the other triangle. This means that the two triangles are congruent. It is “__ASA__” congruent.

**Congruency and Transformations
**A congruent figure may not exactly present the same as the other figure. Transformation of a figure means to change its appearance. Transformation of figures can be rotated, reflected and translated. The figures are transformed but the measures of angles and sides are the same.

**Types of Transformation
**

__Translated__is figures that move up or down or from one side to another.

__Rotated__ is turning a figure from the given point. It is like turning a doorknob. However, the size and shape remain the same.

A __Reflected__ figure appears like a figure in a mirror. It can be right or left inverse.