Chapter 3.2, Problem 13PSA

To determine

To prove : The congruency of $\Delta EFO\cong \Delta KJM$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{EO}\cong \overrightarrow{KM}$

  $\overrightarrow{FO}\cong \overrightarrow{JM}$

  $\overrightarrow{EG}\cong \overrightarrow{KH}$

F is the midpoint of EG

J is the midpoint of KH

Formula used : If all the three sides of any two triangles are congruent, then the triangles are said to be congruent by SSS property

Proof : we know that F is the midpoint of EG. Hence, we can say that

  $\overrightarrow{EF}\cong \overrightarrow{FG}$

And, we also know that J is the midpoint of KH. Hence, we can also say that

  $\overrightarrow{KJ}\cong \overrightarrow{HJ}$

Now, we are given that $\overrightarrow{EG}\cong \overrightarrow{KH}$ , so their halves will also be equal. Thus, we can say that

  $\overrightarrow{EF}\cong \overrightarrow{KJ}$

Now, we know that

  $\overrightarrow{EO}\cong \overrightarrow{KM}$

  $\overrightarrow{FO}\cong \overrightarrow{JM}$

  $\overrightarrow{EF}\cong \overrightarrow{KJ}$

Thus, by SSS property mentioned above, the two triangles are said to be congruent

Hence, the given congruency is proved