Question

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $\Delta ABC$. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Short answer

$\mathit{\Delta }\mathit{A}\mathit{B}\mathit{C}\mathbf{\cong }\mathit{\Delta }\mathit{A}\mathit{K}\mathit{C}$by SSS postulates.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of ASA, SSS, SAS postulates.

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The Side-Side-Side Postulate (SSS) says triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle.

SAS Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent

Step 3. Step description.

From both the triangles $\Delta ABC$and $\Delta AKC$, it is clear that

$\begin{array}{l}AB=KC\\ BC=AK\\ AC=AC\end{array}$

Therefore, the two triangles are congruent with the SSS postulate.

Thus, the triangles are congruent with the SSS postulate.