Rectangle ABCD AB parallel DC prove angle A congurent ANgle B
To prove that angle A is congruent to angle B in rectangle ABCD where AB is parallel to DC, we need to use the properties of rectangles and the corresponding angles formed by parallel lines.
In a rectangle, opposite sides are parallel and congruent, opposite angles are congruent, and adjacent angles are supplementary (add up to 180 degrees).
Step 1: Draw a diagram of the rectangle ABCD with label points A, B, C, and D.
Step 2: Draw a line segment from point A to point C, and from point B to point D.
Step 3: Since AB is parallel to DC, angle ABC is a right angle (90 degrees).
Step 4: Since AB is parallel to DC, angle BCD is also a right angle (90 degrees).
Step 5: In a rectangle, all the angles are right angles, so angle ACB and angle BAD are also right angles (90 degrees).
Step 6: Since angle ABC is a right angle and angle BAD is a right angle, they are congruent (90 degrees = 90 degrees).
Step 7: Similarly, since angle BCD is a right angle and angle BAC is a right angle, they are congruent (90 degrees = 90 degrees).
Step 8: By definition, if two angles are congruent to the same angle, then they are congruent to each other. Therefore, angle A and angle B in rectangle ABCD are congruent.
In conclusion, we have proven that angle A is congruent to angle B in rectangle ABCD where AB is parallel to DC.