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1. Parallelogram

3. Apply the properties of
Parallelogram to solve problems

5. https://www.youtube.com/watch?v=lWACS32YOP8
For practice
https://www.geogebra.org/m/kdd5msu6

6. FG = EH (Opposite sides of a parallelogram are congruent)
= 8
∠ G = ∠E (Opposite angles of a parallelogram are congruent)
= 60°

7. WE ALL KNOW:
WE MUST KNOW:
1.
2.
3. Two adjacent angles of a parallelogram have equal
measure. Find the measure of each of the angles of the
parallelogram.

8. 4. The following figures GUNS and RUNS are
parallelograms. Find x and y. (Lengths are in cm)
GREAT TO KNOW:
SITUATION BASED QUESTION:
5.

9. 1. ∠ T = 80 °(given)
∠ A = 80°(opposite angles are congruent)
∠ S = 180 – 80 = 100° (adjacent angles are supplementary)
∠ F = 100° (opposite angles are congruent)
2. 2x = 10 - 3x (diagonals are bisect each other)
2x+3x = 10
5x = 10
X = 10 ÷ 5
= 2

10. 3. 90°, as they add up to 180°
4. As opposite sides are equal in a parallelogram, 3y – 1 = 26
⇒ 3y -1 = 26
⇒ y = 9
Similarly, 3x = 18 ⇒ x = 6
As you know diagonals bisect each other in a parallelogram,
y + 7 = 20
⇒ y = 20 – 7 = 13
Now, x + y = 16
⇒ x + 13 = 16
⇒ x = 16 – 13 = 3
5.

11. Think and answer………
• In the given figure both RISK and CLUE are
parallelograms. Find the value of x.

12. • In parallelogram RISK
∠ISK = 180° – 120° = 60°(adjacent angles are
supplementary)
Similarly, in parallelogram CLUE
∠CEU = 70°(opposite angles are congruent)
Now, in the triangle
x = 180° – (70°+ 60°) = 50°

14. Find the value of x and y.
Solution:
• Y= 65° (opposite angles are equal)
• X + 4 =12 (opposite sides are equal)
X = 12 – 4
= 8

15. Practice Time
Practice Exercise : 12 A
Q(1 to 7) in Practice Notebook
Page No: 194
From Kaliedoscope

16. 1.One angle of a parallelogram is of measure 70°. Find the
measures of the remaining angles of the parallelogram.
2.Lengths of adjacent sides of a parallelogram is 3 cm and 4 cm.
Find its perimeter.
3. In a parallelogram, the ratio of the adjacent sides is 4 : 5 and
its perimeter is 72 cm then, find the sides of the
parallelogram.
4. The adjacent figure HOPE is a parallelogram. Find the angle
measure x, y and z. State the properties you use to find them.

17. 1. Angle opposite to 70° = 70°
x + x + 70° + 70° = 360°
2x = 360 – 140 = 220°
x = 110°
Four angles are: 70°, 70°, 110°, 110°
2. Since opposite sides are equal, Perimeter = 3 + 4 + 3 + 4 = 14 cm
3. 4x + 5x + 4x + 5x = 72
18x = 72 So, x = 4
Four sides are: 16 cm, 16 cm, 20 cm, 20 cm
4. ∠POH = 110° (linear pair)
x = 110° (opposite angles)
∠EHO = 70° (adjacent angle sum is 180°)
z = 70° - 40° = 30°
y = 40° (alternate interior angles)