# Diagonals of a Parallelogram Divides It into Two Congruent Triangles

## Trending Questions

**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)∘ and (10x+35)∘, 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?

- ∠ABD=40°

∠BDA=40°

∠DAB=100° - ∠ABD=55°

∠BDA=35°

∠DAB=90° - ∠ABD=40°

∠BDA=50°

∠DAB=90° - ∠ABD=45°

∠BDA=45°

∠DAB=90°

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

- x=4∘, y=4∘
- x=3∘, y=4∘
- x=4∘, y=3∘
- x=5∘, y=5∘

**Q.**ABCD is a parallelogram is which ∠ADC=70∘ 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?

Opposite sides are equal.

Opposite sides are parallel.

Adjacent angles are supplementary.

Diagonals bisect each other at 90∘

**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)∘ and (3x−1)∘. 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 ΔABC as shown in figure. Show that BC=12QR.

**Q.**

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

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

- AB and PQ
- AB and QR
- AC and QR
- 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.

45°

65°

75°

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

- Square
- Rectangle
- Trapezium
- Rhombus

**Q.**Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ=135∘ then what is the measure of ∠XWZ and ∠YZW? If l(OY)= 5 cm then l(WY)= ?

**Q.**A theatre, in the shape of a quadrilateral ABCD, has ∠ C=90∘, AB=9 m, BC=12 m, CD=5 m and AD=8 m. If the total area of theatre is 90 m2, then what will be the area of △BAD ?

- 50 m2
- 55 m2
- 60 m2
- 65 m2

**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.

- 5 cm
- 10 cm
- 15 cm
- 20 cm

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

- ∠ABD=55°

∠BDA=35°

∠DAB=90° - ∠ABD=40°

∠BDA=40°

∠DAB=100° - ∠ABD=45°

∠BDA=45°

∠DAB=90° - ∠ABD=40°

∠BDA=50°

∠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 ΔABC as shown in figure. Show that BC=12QR.

**Q.**In the following figure, if m(arc DXE)=90∘ and m(arc AYC)=30∘, find ∠DBE

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

- 2 cm, 4 cm
- 4 cm, 6 cm
- 1 cm, 2 cm
- 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 _____.

- Trapezium
- Kite
- Parallelogram
- None of the above

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

- True
- 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.

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