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Answers
Answer:
1. 110, 110, 70
2. (i) yes ps=rq because opposite sides of parallelogram are equal.
(ii) yes, because opposite side of a parallelogram
Answer:
6.
x=∠HOP=180°-70°(linear pair)=110°
(opposite angles of a parallelogram are equal)
y=∠PHE=40°
(alternate interior angles)
∠PEH+∠EHO=180°(co-interior angles)
110°+40°+z=180°
z=30°
7. (i)
Let O be the point of intersection
BO=DO, CO=AO (∵diagonals of a parallelogram bisect each other)
3x-1=2x+2
3x-2x=3
x=3
Similarily, y=2
(ii)
Let the point of intersection be O
y=40°
Now,
∠ROS=90° (∵diagonals of a rhombus bisect each other perpendicularly)
∠SOR+∠ORS+∠RSO=180° (Angle Sum property)
x=50°
8.
z=∠ADC=180°-70°(linear pair)=110°
(opposite angles of a parallelogram are equal)
y=∠CAD=45°
(alternate interior angles)
∠ADC+∠DAB=180° (co-interior angles)
110°+45°+x=180°
x=25°
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1. Opposite angle=70°
Adjacent angles=110° each
2. (i) yes, opp. sides of a parallelogram are equal
(ii) yes, opp. sides of a parallelogram are equal
(iii) yes, same side
(iv) yes
In ΔPSR and ΔRQP
PS=QR (opp sides of ||gm)
RS=PQ (opp sides of ||gm)
PR=RP (common)
ΔPSR≅ΔRQP (by SSS)
3. Let ABCD be the ||gm
and AB be x
AB=CD=x (opp sides of ||gm)
AD=BC=x+25 (opp sides of ||gm)
Angle sum property
AB+BC+CD+DA=150
4x+50=150
x=25
AB=CD=25cm
AD=BC=50cm
4. 3cm+4cm+3cm+4cm=14cm
Perimeter=14cm
5. Let the ratio constant be x
Perimeter=72cm
AB+BC+CD+DA=72cm
4x+5x+4x+5x=72cm
x=4cm
AB=CD=16cm
AD=BC=20cm
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