In the adjoining figure DC|AB and Angle=B angle=D. Prove triangle=ABC=ADC
To prove that triangles ABC and ADC are congruent, we need to show that they have the same three corresponding sides and the same three corresponding angles.
Here is a step-by-step proof:
Step 1: Given that DC is parallel to AB, and angle B = angle D (given in the problem)
Step 2: In triangle ADC, angle A = angle D (opposite angles are equal)
Step 3: In triangle ABC, angle C = angle B (opposite angles are equal)
Step 4: Using vertical angles, we can say that angle A = angle C (since angle D = angle B)
Step 5: Now, in triangle ADC, we have angle A = angle D and angle A = angle C. This means that angle D = angle C as well.
Step 6: Using the angle-angle-side (AAS) congruence criterion, we can conclude that triangles ABC and ADC are congruent.
Therefore, triangle ABC = triangle ADC.