Chapter 4.3, Problem 4ST1

To determine

To decide whether the given two triangles must be congruent are not?

  

Answer to Problem 4ST1

  $\Delta ACF\cong \Delta DBF$

Explanation of Solution

Given information :

Given two triangles

  

From the diagram, we have $AC=BD,$

  $CF=FD$

  $\angle AFC=\angle DFB\text{Vertically}\text{opposite}\text{angle}$

Thus, the two corresponding sides are equal and one angle is equal in both the triangles.

By Side-Angle-Side (SAS) theorem, we say that the given triangles are congruent.

Hence, $\Delta ACF\cong \Delta DBF$ .