The opposite anglesof a parallelogram are __________________.a)Unequal...
The answer is option 'B' - equal.
Explanation:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Since opposite sides of a parallelogram are parallel, the opposite angles are also equal. In other words, the angles that are across from each other, or diagonally opposite, in a parallelogram are equal.
Proof:
To prove that opposite angles of a parallelogram are equal, we can use the properties of parallel lines and the properties of alternate angles.
Property 1: If two parallel lines are intersected by a transversal, then the alternate interior angles are equal.
This means that if we have two parallel lines and a transversal that intersects them, the angles on the inside of the parallel lines and on opposite sides of the transversal are equal.
Property 2: In a parallelogram, opposite sides are parallel.
This means that if we have a parallelogram, the opposite sides are parallel to each other.
Using the above properties, we can prove that opposite angles of a parallelogram are equal:
1. Let's consider a parallelogram ABCD, where AB is parallel to CD and AD is parallel to BC.
2. Draw diagonal AC, which divides the parallelogram into two triangles, ABC and CDA.
3. According to property 1, angle ABC is equal to angle CDA. Similarly, angle BCD is equal to angle CAD.
4. Since angle ABC is equal to angle CDA and angle BCD is equal to angle CAD, we can conclude that angle ABC is equal to angle BCD.
5. Similarly, we can prove that angle ACD is equal to angle BAD.
6. Therefore, the opposite angles of a parallelogram are equal.
Hence, the correct answer is option 'B' - equal.
The opposite anglesof a parallelogram are __________________.a)Unequal...
Equal
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