Question

In a figure given below, which congruence rule can be used to prove $\Delta ABC \cong \Delta ADC$ ?

Answer 1

Hint: First take a look at the given figure and find what is common in both the triangles $\Delta ABC$ and $\Delta ADC$, then find the rule that makes both the triangles congruent to each other.

Complete answer:
We have to find the rule of congruence that shows that$\Delta ABC \cong \Delta ADC$.
It is given in the figure that the side $AD$ is equal to the side $BC$ and the side $AB$ is equal to the side $CD$.
Now, take a look at the triangles $\Delta ABC$ and $\Delta ADC$, the sides $AD$ is equal to the side $BC$ and the side $AB$ is equal to the side $CD$ and there is a common side in both the triangles, named $AC$.
$AB = CD$(Given in the figure)
$AD = BC$(Given in the figure)
$AC = AC$(Common side of both triangles)
It can be seen that three sides in both the triangles are the same. Then there is a congruence named as $SSS$, which stands “side-side-side”.
The three sides of both the triangles have the same length, then according to SSS congruence, the triangles $\Delta ABC$ and $\Delta ADC$ are congruent to each other. That is,
$\Delta ABC \cong \Delta ADC$
This is the desired result that the problem is asked to show.

Note: There are five types of congruency, named as SSS, SAS, ASA, AAS, and HL. The name of these congruency rules defines their property as:
SSS defines “side-side-side”
SAS defines “side-angle-side”
ASA defines “angle-side-angle”
AAS defines “angle-angle-side”
HL defines “hypotenuse-leg”
If these defined rules are common in any two triangles then these triangles are said as congruent applying the congruence rule.