The triangles ADC and EBC are congruent by the AAS axiom as two angles and one side of these triangles are equal. Hence, 2nd option is the right choice.
What are congruent triangles?
Congruent triangles are pairs of triangles that have the same shape and size.
What are the different axioms of congruency of triangles?
Triangles can be proved congruent using the following axioms:
- SSS axiom (All sides are equal)
- SAS axiom (Two sides and the angle containing those sides are equal)
- ASA axiom (Two angles and the common side are equal)
- AAS axiom (Two angles and one side are equal)
- RHS axiom (In a right-angled triangle, the hypotenuse and any one leg are equal).
How do we solve the given question?
We are given a figure, showing two triangles ADC and EBC.
We are asked to check whether the given triangles are congruent.
Now, in ΔADC and ΔEBC,
∠A = ∠E (shown in the figure)
DC = BC (shown in the figure)
∠C is common.
∴ ΔADC ≅ ΔEBC (by AAS axiom, as two angles and one side are equal).
∴ The triangles ADC and EBC are congruent by the AAS axiom as two angles and one side of these triangles are equal. Hence, 2nd option is the right choice.
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