Download App

Area Theorems [Proof and Use] — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSArea Theorems [Proof and Use]4 Marks
Question
The given figure shows a rectangle $\text{ABDC}$ and a parallelogram $\text{ABEF};$ drawn on opposite sides of $AB.$Prove that$:(i)$ Quadrilateral $\text{CDEF}$ is a parallelogram Area of the quad. $\text{CDEF}= $Area of rect. $\text{ABDC} +$ Area of $\|gm. ABEF.$
✓

Answer

After drawing the opposite sides of $AB$, we get

Since from the figure, we get $CD\|FE,$ therefore, $FC$ must parallel to $DE.$
Therefore it is proved that the quadrilateral $CDEF$ is a parallelogram.
The area of the parallelogram on the same base and between the same parallel lines is always equal and the area of the parallelogram is equal to the area of a rectangle on the same base and of the same altitude.
i.e, between the same parallel lines.
So Area of $\text{CDEF}=$ Area of $\text{ABDC} +$ Area of $\text{ABEF}$
Hence Proved

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 "[4 marks sum]" from Area Theorems [Proof and Use]→Area Theorems [Proof and Use] — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Use the given figure to find:$(i) \tan \theta^{\circ}(ii) \theta^{\circ}(iii) \sin ^2 \theta^{\circ}-\cos ^2 \theta^{\circ}(iv)$ Use $\sin \theta^{\circ}$ to find the value of $x$.
→
Draw the graph of the equation 2x - 3y = 5.
(i) Find the value of y, when x = 4.
(ii) Find the value of x, when y = 3.
[Hint. Take the scale 1 unit = 3 divisions.]
→
Evaluate, correct to one place of decimal, the expression$\frac{5}{\sqrt{20}-\sqrt{10}}$, if $\sqrt{5}=2.2$ and $\sqrt{10}=3.2$
→
If $\left(x+\frac{1}{x}\right)=6$, find the values of  $\left(x^2-\frac{1}{x^2}\right)$.
→
In the given figure, $\angle QPR = 50^\circ $ and $\angle PQR = 60^\circ $. Show that: $SN < SR$
​​​​​​​
→
Image
Find the perimeter and area of quadrilateral ABCD in which AB = 9cm, AD = 12cm, BD = 15 cm, CD = 17cm and $\angle CBD =90^{\circ}$
→
Make $k$ the subject of formula $T=2 \pi \sqrt{\frac{ k ^2+ h ^2}{h g}}$
→
In $\triangle ABC, D, E$ and $F$ are the midpoints of $AB, BC$ and $AC$.Show that $AE$ and $DF$ bisect each other.
→
The present population of a town is 176400. If the rate of growth in its population is 5% per annum, find:
(i) its population 2 years hence,
(ii) its population one year ago.
→
Solve :$\frac{20}{x+y}+\frac{3}{x-y}=7 ,\frac{8}{x-y}-\frac{15}{x+y}=5$
→