Question

many shapes can be congruent. Triangles is one of them. What are the various ways to prove triangle congruency? Where in the real world would it be important for you to apply these concepts?

Answer 1

For triangles to be congruent, they must have the same angles and same three sides, irrespective of what direction they are pointing to.

Following are the ways to find if two triangles are congruent:

1. SSS (side, side, side): If all three sides of a triangle are equal to the three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side): If the two sides and the included angle of a triangle are equal to the corresponding sides and the angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle): If the two angles and their shared side is equal to the corresponding angles and shared side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side): If two angles and the non-included side of a triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg): If the hypotenuse and one leg (side other than hypotenuse) of a right angle triangle are equal to the corresponding hypotenuse and the leg of another right angle triangle, then the two triangles are congruent.

Congruent triangles are used in real world for construction purposes to ensure that the man-made structures are strong and stable enough.