Question
Show that a diagonal divides a parallelogram into two triangles of equal area.
✓
Answer
Let ABCD be a parallelogram and BD be its diagonal. To prove:$\text{ar}(\triangle\text{ABD})=\text{ar}(\triangle\text{CDB})$Proof: In $\triangle\text{ABD}$ and $\triangle\text{CDB},$ we have : AB = CD [Opposite sides of a parallelogram] AD = CB [Opposite sides of a parallelogram] BD = DB [Common] i. e., $\triangle\text{ABD}\cong\triangle\text{CDB}$ [SSS criteria]$\therefore\ \text{ar}(\triangle\text{ABD})=\text{ar}(\triangle\text{CDB})$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If O is the centre of the circle, find the value of x in the following figures:
In figure ABC and BDE are two equilateral triangles such that D is the midpoint of BC. AE intersects BC in F. Prove that: 
$\text{ar}(\triangle\text{FED})=\frac{1}{8}\text{ar}(\triangle\text{AFC})$
→$\text{ar}(\triangle\text{FED})=\frac{1}{8}\text{ar}(\triangle\text{AFC})$Write the subset relations between the following sets.
X = set of all quadrilaterals.
Y = set of all rhombuses.
S = set of all squares.
T = set of all parallelograms.
V = set of all rectangles.
X = set of all quadrilaterals.
Y = set of all rhombuses.
S = set of all squares.
T = set of all parallelograms.
V = set of all rectangles.
In the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
$f(x)=2 x^3-9 x^2+x+12, g(x)=3-2 x$
→$f(x)=2 x^3-9 x^2+x+12, g(x)=3-2 x$
The monthly profits (in ₹) of 100 shops are distributed as follows:
Draw a histogram for the data and show the frequency polygon for it.
|
Profits per shop:
|
0-50
|
50-100
|
100-150
|
150-200
|
200-250
|
250-300
|
|
No. of shops:
|
12
|
18
|
27
|
20
|
17
|
6
|
Find the remainder when $x^3+3 x^3+3 x+1$ is divided by: $x+\pi$
→Write two solutions for the following equations:$\text{x}+\pi\text{y} = 4 $
→In figure, ABCD, ABFE and CDEF are parallelograms. Prove that $\text{ar}(\triangle\text{ADE})=\text{ar}(\triangle\text{BCF}).$
→Factorize the following expressions:
$8a^3 - b^3 - 4ax + 2bx$
→$8a^3 - b^3 - 4ax + 2bx$
In the given figure, O is the canter of the circle and $\angle\text{AOB}=70^\circ.$ Calculate the values of
→- $\angle\text{OCA}$
- $\angle\text{OAC}$