ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area Class 9

ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area Class 9

Question 1.

ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area (∆PCD): area (∆QCD)? Class 9

Solution:

Draw perpendicular PM and QN to CD .

∠ABCD is a parallelogram ...[Given]

AB || CD ... [opposite sides are parallel]

P and Q lie on side AB ... [Given]

∴ Perpendicular distance from P and Q to CD will be equal

∴ PM = QN ...(i)

Also, Area of triangle = $\frac{1}{2}$ × base × height

∴ ∆PCD and ∆QCD have same base CD

$\therefore \quad \frac{\operatorname{area}(\triangle \mathrm{PCD})}{\operatorname{area}(\triangle \mathrm{QCD})}=\frac{\frac{1}{2} \times \mathrm{CD} \times \mathrm{PM}}{\frac{1}{2} \times \mathrm{CD} \times \mathrm{QN}}=\frac{\mathrm{PM}}{\mathrm{QN}}=1 \ldots[$ From (i) $]$

∴ Area (∆PCD): area (∆QCD) = 1.