Chapter 4, Problem 28SGR

To determine

To prove: $\Delta ABX\cong \Delta DCX$

Answer to Problem 28SGR

SAS Congruence Postulate.

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The figure can be drawn as:

  

All the angles at the central point have the same measure, therefore, $\angle AXB\cong \angle CXD$

All sidewalks are of equal length leading to the central point, therefore,

  $\begin{array}{l}\overline{XA}\cong \overline{XC}\\ \text{and}\\ \overline{XB}\cong \overline{XC}\end{array}$

Hence, $\Delta ABX\cong \Delta DCX$ according to SAS Congruence Postulate.