Download App

Areas Of Parallelograms And Triangles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsAreas Of Parallelograms And Triangles3 Marks
Question
ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersects AB at P and DC at Q. Prove that $\text{ar}(\triangle\text{POA})=\text{ar}(\triangle\text{QOC}).$
✓

Answer

In triangles POA and QOC, we have$\angle\text{AOP}=\angle\text{COQ}$
$\text{AO}=\text{OC}$
$\angle\text{PAC}=\angle\text{QCA}$
So, by ASA congruence criterion, we have$\triangle\text{POA}\cong\triangle\text{QOC}$
$\Rightarrow\text{ar}(\triangle\text{POA})=\text{ar}(\triangle\text{QOC}).$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Mark Question" from Areas Of Parallelograms And Triangles→Areas Of Parallelograms And Triangles — all question types→Maths STD 9 question papers→Maharashtra Board STD 9 question papers→Maharashtra Board question paper generator→

Similar questions

P is any point on the diagonal AC of a parallelogram ABCD. Prove that $\text{ar}(\triangle\text{ADP})=\text{ar}(\triangle\text{ABP}).$
→
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
→
What must be added to $2 x^4-5 x^3+2 x^2-x-3$ so that the result is exactly divisible by $(x-2) ?$
→
The perimeter of a parallelogram is 22cm. If the longer side measures 6.5cm, what is the measure of shorter side?
→
The diameter of a copper sphere is 18cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108m, find its diameter.
→
Find the median of the data:
12, 17, 3, 14, 5, 8, 7, 15
→
A shopkeeper has one laddoo of radius 5cm. With the same material, how many laddoos of radius 2.5cm can be made?
→
Find the following products:
$(2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + 6ab - 6bc + 4ca)$
→
If $\text{x}=3+2\sqrt{2},$ check whether $\text{x}+\frac{1}{\text{x}}$ is rational or irrational.
→
A 4cm cube is cut into $1cm$ cubes. Calculate the total surface area of all the small cubes.
→