The Triangles Shown Below Must Be Congruent

What Does Congruent Mean?

Congruence is a concept in mathematics that states that two objects are congruent when they can be put on top of each other and have the same size, shape, and orientation. This means that for two shapes to be congruent, they must have the same number of sides and the same angle measurements.

How Can We Tell If Two Triangles Are Congruent?

There are several ways to determine if two triangles are congruent. The most common is to use the Side-Side-Side (SSS) theorem. This theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Other Theorems To Prove Congruence

The Side-Angle-Side (SAS) theorem states that if two sides of a triangle and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. The Angle-Angle-Side (AAS) theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

How To Use Theorems To Prove Congruence

To use these theorems to prove that the two triangles in the picture are congruent, we need to start by looking at the measurements of the sides and angles of the two triangles. If we compare the measurements, we can see that the two triangles have the same three sides and two angles, which means that they are congruent according to the SAS theorem. Therefore, the triangles in the picture must be congruent.

Conclusion

In conclusion, two triangles are congruent when they have the same size, shape, and orientation. To prove that two triangles are congruent, we can use the Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Angle-Side (AAS) theorem. By comparing the measurements of the sides and angles of two triangles, we can determine if they are congruent or not.