EXERCISE 19 B
Question 1
In a parallelogram PQRS, ∠S=75° .Determine the measures of ∠P and ∠Q.
Sol :
Question 2
The measures of two adjacent angles of a parallelogram are in the ratio 2:7. Find the measure of each of the parallelogram.
Sol :
Question 3
Two opposite angles of a parallelogram are 6x-17° and x+63°. Find the measure of each angle of the parallelogram.
Sol :
Question 4
Can a quadrilateral ABCD be a parallelogram , if
(i) AB=DC=5cm, AD=3.8cm and BC=3.6cm
(ii) ∠A=95° , ∠B=75°
(iii) ∠B=105° , ∠D=75°
Sol :
Question 5
EFGH is a parallelogram.Find x, y and z . Also , state the properties you use to find them.
Sol :
Question 6
ABCD and EFGH are parallelograms. Find the measure of x
Sol :
Question 7
PQRS is a parallelogram. Find x and y. The given lengths are in cm
Sol :
Diagonals bisect each other in parallelogram
∴x+7=20
x=20-7=13
also, x+y=16
13+y=16
y=16-13=3
Question 8
In a ΔABC, D, E, F are respectively, the mid-points of BC , CA and AB. If the lengths of sides AB,BC and CA are 17 cm, 18 cm and 19 cm respectively, find the perimeter of ΔDEF
Sol :
The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.
Question 9
In the figure, ABCD is a parallelogram in which ∠A=60°. If the bisectors of ∠A and ∠B meet at P,prove that AD=DP,PC=BC and DC=2AD
Sol :
Question 10
In the figure, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF=2AB.
Sol :
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