Parallelogram
It is a quadrilateral with two pairs of parallel sides.
Properties and important points to remember-
Opposite sides of a parallelogram are equal in length.
Opposite angles of a parallelogram are equal in measure. (More text below video...)
(Continued from above)
Opposite sides of a parallelogram can never intersect.
The diagonals of a parallelogram bisect each other.
Consecutive angles are supplementary, add to 180°.
Area (A), of a parallelogram is A = bh,
where is the base and is height of parallelogram.
The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
A parallelogram is a quadrilateral with opposite sides parallel and congruent.
Notice that:
A rectangle is a parallelogram, but with each angle as 90°.
A rhombus is a parallelogram, but with all sides equal in length.
A square is a parallelogram but with all sides equal in length, and each angle at 90°
Example 2: Given- the figure below shows the dimensions of side and diagonal of the parallelogram ABCD. The measure of angles A and C
are each 45°. Find out the area of ABCD.
Study and analyze the given information carefully.
Step 1: ABCD is a parallelogram, as both the opposite sides are equal.
AB = CD and AD = BC.
Step 2: Use the formula A = length * height. Now calculate the length and height.
Step 3: AD2 = (52)2 + (52)2= 100.
Thus AD = 10 (taking sq root on both sides).
Step 4: Drop the perpendicular from B, which will create 45°, 45°, and 90° triangle. The hypotenuse of that triangle will be AB.
Step 5: You know that sides of this special triangle shall be in the ratio of 1:1:2.
From this height of this triangle will be 5.
Step 5: Area thus equals = 5 * 10 =50 units, as the final answer.
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