Question

Match the Congruence Theorem that describes how the two triangles are congruent.

Answer 1

the theorems that explain congruence in the given triangles are:

fig 1 -SSS

fig 2-SAS

fig 3-ASA

fig 4-AAS

What is congruence in triangle?

if two triangles have the same number of sides and angles, they are said to be congruent. However, only three of these six angles and sides need to be examined in order to determine whether the three are congruent. The five congruent triangle theorems are therefore SSS, SAS, AAS and ASA.

1. The reason why it is SSS in figure 1 is because the three sides of one are equal to the three sides of the other.
2. Figure 2 follows SAS indicates that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
3. Figure 3 follows ASA theorem, first triangle's two angles and side that is included between its angles are equivalent to the second triangle's corresponding two angles and side, which is why the equation is asa.
4. In figure 4 follows AAS theorem, two angles from one triangle and a non-included side from another triangle are congruent, which is why the symbol aas is used.

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