Chapter 4.3, Problem 22PPS

To determine

To prove: To prove congruence of triangles is transitive

Explanation of Solution

Given information:

  $\Delta EFG\cong \Delta JKL\left(\overline{EF}\cong \overline{JK}\right),\Delta ABC\cong \Delta JKL\left(\overline{AB}\cong \overline{JK}\right)$

Proof:

  

The transitive property of triangle states that if two triangles are both congruent to a third triangle, then the first two triangles are also congruent.

It is given that $\overline{EF}\cong \overline{JK}$ and $\overline{AB}\cong \overline{JK}$ which means that the measure of two sides of a triangle should be equal if they are congruent according to definition of congruent segments. So, if $EF=JK$ and $AB=JK$ then according to transitive property of equality $EF=AB$ .

Hence, by applying definition of congruent segments we get $\overline{EF}\cong \overline{AB}$ .

So, we can say that $\Delta ABC\cong \Delta EFG\left(\overline{AB}\cong \overline{EF}\right)$ .

Hence, it is proved that congruence of triangles is transitive.