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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
Parallelogram

Properties of a Parallelogram:

1. In a parallelogram any two opposite sides are equal.
2. In a parallelogram any two opposite angles are equal.
3. In a parallelogram the diagonals bisect each other.
4. In a parallelogram, each diagonal divides it into two congruent triangles.
5. In a parallelogram, any two adjacent angles have their sum equal to 180, that is, they are supplementary.


THEOREMS:
1. A quadrilateral is a parallelogram, then its opposite sides are congruent;

If ABCD is a parallelogram, then AB @ CD and BC @ AD
2. A quadrilateral is a parallelogram, then its opposite angles are congruent;

If ABCD is a parallelogram, then A @ C and B @ D.
3. A quadrilateral is a parallelogram, then its consecutive angles are supplementary;

x + y = 1800
4. A quadrilateral is a parallelogram, then its diagonals bisect each other.

5. One pair of opposite sides are equal and parallel;
Special types of parallelograms: rhombus, rectangle, square
A quadrilateral is a rhombus if and only if it has four congruent sides.
A quadrilateral is a rectangle if and only if it has four right angles.
A quadrilateral is a square if and only if it is a rhombus and rectangle.
A parallelogram is a rhombus, if and only if its diagonals are perpendicular.
A parallelogram is a rhombus, if and only if each diagonal bisects a pair of opposite angles.
A parallelogram is a rectangle, if and only if its diagonals are congruent.

Example:
In a parallelogram ABCD A = 60. Find the remaining angles.
Solution:
We know that the opposite angles of a parallelogram are equal. So A = C = 60.
Two adjacent angles of a parallelogram have their sum equal to 180.
Now both B and D are adjacent to A.
\ B = D = 180 - 60 = 120.
\ The remaining angles are 100, 80 and 100.


Directions: Draw a parallelogram and answer the following questions.
1) Parallelogram of lengths 5, 12, 5, x+4 cm. Find the value of x.
2) Parallelogram of angles 600, 1200,600, 2x0. Find the value of x.
3) Parallelogram with supplementary angles of 2x0, 4x0. Find the value of x.

Q 1: In a parallelogram ABCD, angle A = 85 degrees. Find the remaining angles.
60, 120 and 60 degrees Respectively
110, 70 and 110 degrees Respectively
95, 85 and 95 degrees Respectively
100, 80 and 100 degrees Respectively

Q 2: Find the value of m in the figure.

12
6
5

Q 3: In a parallelogram ABCD, angle A = 70 degrees. Find the remaining angles.
110, 70 and 110 degrees Respectively
100, 80 and 100 degrees Respectively
60, 120 and 60 degrees Respectively
95, 85 and 95 degrees Respectively

Q 4: In a parallelogram ABCD, angle A = 80 degrees. Find the remaining angles.
100, 80 and 100 degrees Respectively
95, 85 and 95 degrees Respectively
70, 110 and 70 Respectively
110, 70 and 110 degrees Respectively

Q 5: In a parallelogram ABCD, angle A = 65 degrees. Find the remaining angles.
60, 120 and 60 degrees Respectively
100, 80 and 100 degrees Respectively
115, 65 and 115 degrees Respectively
110, 70 and 110 degrees Respectively

Q 6: In a parallelogram ABCD, angle A = 120 degrees. Find the remaining angles.
95, 85 and 95 degrees Respectively
60, 120 and 60 degrees Respectively
100, 80 and 100 degrees Respectively
110, 70 and 110 degrees Respectively

Q 7: Find the value of x in the figure.

Answer:

Q 8: Find the value of x in the figure.

30
50
45

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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