Diagonals of a Parallelogram Divides It into Two Congruent Triangles

Q.

Find the area of the triangle two sides of which are $18cm$ and $10cm$ and the perimeter is $42cm$.

Q.

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side $a$. Find the area of the signal board, using Heron’s formula. If its perimeter is $180cm$ what will be the area of the signal board?

Q. Question 16
If two adjacent angles of a parallelogram are $(5x-5{)}^{\circ }$ and $(10x+35{)}^{\circ }$, then the ratio of these angles is ___________.
a) 1 : 3
b) 2 : 3
c) 1 : 4
d) 1 : 2

Q. Consider a square ABCD that has a diagonal BD. What will be the measure of each angle of the $△ABD$ formed?

1. $\angle ABD=40°$
   $\angle BDA=40°$
   $\angle DAB=100°$
2. $\angle ABD=55°$
   $\angle BDA=35°$
   $\angle DAB=90°$
3. $\angle ABD=40°$
   $\angle BDA=50°$
   $\angle DAB=90°$
4. $\angle ABD=45°$
   $\angle BDA=45°$
   $\angle DAB=90°$

Q. In the given parallelogram ABCD, find the value of $x$ and $y.$

1. $x=4^{\circ },y=4^{\circ }$
2. $x=3^{\circ },y=4^{\circ }$
3. $x=4^{\circ },y=3^{\circ }$
4. $x=5^{\circ },y=5^{\circ }$

Q. ABCD is a parallelogram is which $\angle ADC={70}^{\circ }$ and side AB is produced to point E as shown in the figure. Find $x+y.$

Q.

Which among the following is sufficient to prove that a quadrilateral is a parallelogram?

1. Opposite sides are equal.

2. Opposite sides are parallel.

3. Adjacent angles are supplementary.

4. Diagonals bisect each other at ${90}^{\circ }$

Q.

A triangle with an area of $10$ square meters has a base of $4$ meters. A similar triangle has an area of $90$ square meters. What is the height of the larger triangle?

Q. Question 37
If the adjacent angles of a parallelogram are equal, then the parallelogram is a
a) Rectangle
b) Trapezium
c) Rhombus
d) None of these

Q. Question 138
The adjacent angles of a parallelogram are $(2x-4{)}^{\circ }$ and $(3x-1{)}^{\circ }$. Find the measures of all angles of the parallelogram.

Q.

Find the area of the triangle whose sides are $42cm,39cm,45cm$

Q.

Find the area of the triangle whose base is $8cm$ and height is$11cm.$

Q. Question 7
Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.

Q.

Find the area of the triangle whose sides are $52cm,60cm,56cm$

Q. If two congruent triangles $△ABC\text{and}△PQR$ are joined together so as to form a parallelogram, then which corresponding sides of the two triangles are joined together?

1. AB and PQ
2. AB and QR
3. AC and QR
4. BC and PQ

Q.

Find the area of the triangle if its sides are $21cm,17cm,10cm.$

Q.

The area of the triangle is $216c{m}^2.$One triangle measures is $24cm$. Find the distance of the corresponding vertex from the side.

Q.

In the figure given below, ABCD is a parallelogram. From the given options, select what could be the values of either $x$ or $y$.

1. 45°

2. 65°

3. 75°

4. 80°

Q.

The height of a triangle is $4$ inches more than twice the length of the base. The area of the triangle is $35$ square inches. What is the height of the triangle?

Q. The angle-bisectors of a parallelogram form a quadrilateral as shown in the figure given below,
Then ABCD is a .

1. Square
2. Rectangle
3. Trapezium
4. Rhombus

Q. Diagonals of a parallelogram WXYZ intersect each other at point O. If $\angle XYZ={135}^{\circ }$ then what is the measure of $\angle XWZand\angle YZW?$ If l(OY)= 5 cm then l(WY)= ?

Q. A theatre, in the shape of a quadrilateral ABCD, has $\angle C={90}^{\circ }$, $AB=9m,BC=12m,CD=5mandAD=8m$. If the total area of theatre is $90m^2$, then what will be the area of $△BAD?$

1. $50m^2$
2. $55m^2$
3. $60m^2$
4. $65m^2$

Q. ABCD is a rhombus. Length of the diagonal BD is half the length of AB. The perimeter of rhombus ABCD is 80 cm. Find the length of BO.

1. 5 cm
2. 10 cm
3. 15 cm
4. 20 cm

Q. Consider a square ABCD that has a diagonal BD. What will be the measure of each angle of the $△ABD$ formed?

1. $\angle ABD=55°$
   $\angle BDA=35°$
   $\angle DAB=90°$
2. $\angle ABD=40°$
   $\angle BDA=40°$
   $\angle DAB=100°$
3. $\angle ABD=45°$
   $\angle BDA=45°$
   $\angle DAB=90°$
4. $\angle ABD=40°$
   $\angle BDA=50°$
   $\angle DAB=90°$

Q. Question 7
Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.

Q. In the following figure, if $m($arc $DXE)={90}^{\circ }$ and $m($arc $AYC)={30}^{\circ }$, find $\angle DBE$

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 2 cm, 4 cm
2. 4 cm, 6 cm
3. 1 cm, 2 cm
4. 3 cm, 4 cm

Q. If the diagonals of a quadrilateral ABCD bisect each other at the point O then the quadrilateral ABCD can be a _____.

1. Trapezium
2. Kite
3. Parallelogram
4. None of the above

Q. A diagonal of a parallelogram divides it into two congruent triangles.

1. True
2. False

Q. Given below is a parallelogram. AC and BD are diagonals. If AO = x + y, OC = 5y, DO = 3x, OB = 12, then find x and y.

1. x = 2, y = 3
2. x = 1, y = 4
3. x = 3, y = 2
4. x = 4, y = 1