Opposite Angles of a Parallelogram are Equal
Opposite Angles of a Parallelogram are Equal
Theorem 3: The opposite angles of a parallelogram are equal. GIVEN A parallelogram ABCD To prove <A = <C and <B = <D Proof Since ABCD is a parallelogram. Therefore, AB Now, AB
Again, AD
From (i) and (ii), we get <A + <D = <D + <C
Similarly, <B = <D. Hence, <A = <C and <B = <D |  | |
| Converse Theorem: A quadrilateral is a parallelogram if its opposite angles are equal | ||
Given : A quadrilateral ABCD in which To Prove: ABCD is a Parallelogram. Proof: In a quadrilateral ABCD Adding (1) and (2)
Now Using equation (3) we get But As their sum is Again But As their sum is From (4) and (5) AD || BC and AB || CD Hence ABCD is a a parallelogram | | |
Illustration: Find all the angles of the parallelogram ABCD the figure given. Solution: In triangle BCD
5x+ 20+ 2x+ 10 +3x= 180 10x+ 30 = 180 10x = 180-30=150 x= 15 In a parallelogram sum of adjacent angles= 180 In a parallelogram opposite angles are equal
Hence |  | |
In the following figure, ABDC, ABFE are parallelograms. Which of the following is true about the angles of this parallelogram?
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| Right Option : D | |||
| View Explanation | |||
In the following figure, If ABCD is a parallelogram, then which angles are equal?
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| Right Option : D | |||
| View Explanation | |||
In the following figure, which of the angles will be equal if PQRS is a parallelogram?
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| Right Option : B | |||
| View Explanation | |||
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