Question

Complete each sentence with the most appropriate word, phase or value.

If a diagonal of an equilateral is draw, the two triangles formed cab be proved congruent by the ________ method.

Short answer

The answer is SSS Postulate.

Step-by-step solution

- Consider the diagram. 

Since, the quadrilateral is equilateral, so, all the sides are congruent:

$\overline{PQ}\cong \overline{QS}\cong \overline{SR}\cong \overline{PR}$.

- State the explanation.

In the diagram, when the diagonal is draw, it divides the quadrilateral into two triangles, whose two sides are congruent and the remaining side is the diagonal, which is same for both.

In $\Delta PQR$ and $\Delta SQR$:

$\begin{array}{l}\overline{PQ}\cong \overline{SQ}\\ \\ \overline{QR}\cong \overline{QR}\\ \\ \overline{PR}\cong \overline{SR}\end{array}$

So, both the triangles are congruent by SSS postulate.

- State the conclusion.

Therefore,“If a diagonal of an equilateral is draw, the two triangles formed cab be proved congruent by the SSS Postulate method.”