Question on Congruent Triangles

Topic : Congruent Triangle

Question : Define Congruent Triangle and Explain how to decide Triangle to be congruent triangle

Solution :
Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.
Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are congruent. Various groups of three will do. Triangles are congruent if:
1. SSS (side side side) All three corresponding sides are equal in length.
2. SAS (side angle side) A pair of corresponding sides and the included angle are equal.
3. ASA (angle side angle) A pair of corresponding angles and the included side are equal.
4. AAS (angle angle side) A pair of corresponding angles and a non-included side are equal.
5. HL (hypotenuse leg of a right triangle) Two right triangles are congruent if the hypotenuse and one leg are equal.

Note : If all the corresponding angles of a triangle are the same, the triangles will be the same shape, but not necessarily the same size. In the figure on the right, the triangles have the same angles and look the same shape, but are not congruent because they are not the same size. They are called similar triangles.