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If ABCD is a Parallelogram with 2 Adjacent angles ∠A =∠B, then the parallelogram is a
- a)Rhombus
- b)Triangle
- c)Rectangle
- d)Square
Correct answer is option 'C'. Can you explain this answer?
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If ABCD is a Parallelogram with 2 Adjacent angles∠A =∠B, then ...
If ABCD is a parallelogram, then opposite sides are equal in length and opposite angles are equal in measure.
Since ABCD is a parallelogram, we can say that angle A + angle C = 180 degrees (since consecutive angles of a parallelogram are supplementary).
If we are given that angle A and angle B are adjacent angles, then we can say that angle A + angle B = 180 degrees (since adjacent angles form a straight line).
Thus, we can conclude that angle A + angle C = angle A + angle B.
By subtracting angle A from both sides of the equation, we get angle C = angle B.
Therefore, angle B and angle C are equal in measure.
Since ABCD is a parallelogram, we can say that angle A + angle C = 180 degrees (since consecutive angles of a parallelogram are supplementary).
If we are given that angle A and angle B are adjacent angles, then we can say that angle A + angle B = 180 degrees (since adjacent angles form a straight line).
Thus, we can conclude that angle A + angle C = angle A + angle B.
By subtracting angle A from both sides of the equation, we get angle C = angle B.
Therefore, angle B and angle C are equal in measure.
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If ABCD is a Parallelogram with 2 Adjacent angles∠A =∠B, then the parallelogram is aa)Rhombusb)Trianglec)Rectangled)SquareCorrect answer is option 'C'. Can you explain this answer?
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