Chapter 4, Problem 9CUR

To determine

Fill in the blank with appropriate word/phrase.

Answer to Problem 9CUR

SSS Postulate.

Explanation of Solution

Given:

If a diagonal of an equilateral quadrilateral is drawn , the two triangles formed can be proved congruent by the _____ method.

Calculation:

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

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

  

When the diagonal is drawn , 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 $\Delta PQR\text{ and }\Delta \text{SQR}$ :

  $\overline{PQ}\cong \overline{SQ}$

  $\overline{QR}\cong \overline{QR}$

  $\overline{PR}\cong \overline{SR}$

So, both of the triangles are congruent by SSS Postulate.