# Construction of a Quadrilateral When Other Special Properties Are Known

## Trending Questions

**Q.**

Question 3

Construct the Parallelogram MORE where

OR=6 cm, RE= 4.5 cm, EO = 7.5 cm

**Q.**The point where the medians of a triangle are concurrent is called the ____. Fill in the blank with the most appropriate answer.

- circumcenter
- orthocenter
- centroid
- incenter

**Q.**

Diagonals of a parallelogram are perpendicular to each other.

Is this statement true?

Give reason for your answer.

- True
- False

**Q.**What is the minimum number of measurements are required for the construction of a rectangle?

- 3
- 4
- 1
- 2

**Q.**Steps for the construction of a parallelogram ABCD with sides AB = 4 cm and AD = 5 cm and angle A =60∘ are given below.

Choose the correct order.

1. Construct a line segment AB = 4 cm and construct a 60∘ angle at point A.

2. Mark the intersecting point as C. Join C to D and B to C.

3. Draw an arc of radius 4 cm and D as centre to intersect the arc drawn in step 2.

4. Construct a line segment AD = 5 cm on the other arm of the angle. Then draw an arc of radius 5 cm and B as centre.

- 1, 4, 3, 2
- 1, 2, 3, 4
- 1, 3, 2, 4
- 1, 4, 2, 3

**Q.**

The adjacent sides of a rectangle are:

Coincident

Perpendicular

Parallel

Concurrent

**Q.**

Question 1

Construct the square READ with RE = 5.1 cm.

**Q.**

What is the minimum number of measurements required to construct a unique rhombus?

**Q.**

Question 3

Construct a rectangle with adjacent sides of length 5cm and 4cm.

**Q.**

Construct a quadrilateral ABCD given AB = 5.1 cm, AD = 4 cm, BC = 2.5 cm, ∠A=60∘ and ∠B=85∘ [2 MARKS]

**Q.**Construct a rhombus ROSE with RO = 5 cm and RS = 8 cm.

**Q.**

Question 4

Construct a parallelogram OKAY where OK=5.5 cm and KA=4.2 cm.

**Q.**ntIn any triangle ABC, prove the following: a(cosB.cosC+cosA) = b(cosC.cosA+cosB) = c(cosA.cosB+cosC)n

**Q.**Construct a parallelogram ABCD such that l(BC) = 7 cm, m∠ABC = 40$\xb0$, l(AB) = 3 cm.

**Q.**

Question 2

Construct the rhombus whose diagonals are 5.2 cm and 6.4 cm.

**Q.**

We have a parallelogram ABCD with AC and BD as diagonals. In parallelogram ABCD, ∠ ABC = 110∘, ∠ DAC = 15∘, ∠ CAB=25∘, AB = 5cm, CD = 7cm. Can we construct this parallelogram?

With ADC, yes

No, it is impossible

Yes, of course

With AC, yes

**Q.**Steps for the construction of a parallelogram ABCD in which AB = 6 cm, BC = 4.5 cm and diagonal AC = 6.8 cm is given below.

Choose the correct order.

1. Draw AB = 6 cm.

2. With A as centre and radius 6.8 cm, draw an arc.

3. With A as centre and radius 4.5 cm, draw an arc.

4. With B as center and radius 4.5 cm draw another arc, cutting the previous arc at C. Join BC and AC.

5. With C as centre and radius 6 cm draw another arc, cutting the previously drawn arc at D. Join DA and DC.

- 1, 2, 4, 3, 5
- 1, 2, 3, 4, 5
- 1, 2, 5, 4, 3
- 1, 2, 3, 5, 4

**Q.**Explain about the properties of the following quadrilaterals:-

**Q.**The point of intersection of angle bisectors is known as

- Incentre
- Orthocentre
- Centroid
- Circumcentre

**Q.**

Median is a line joining the ________ to the midpoint of the opposite side.

centre

vertex

random point inside the triangle

random point on the sides of a triangle

**Q.**

Ankush prepared a poster in the form of a parallelogram, as in the figure.

(i) If ∠A=(5x+7)∘ and ∠B=(3x−3)∘, find all the angles of parallelogram ABCD.

(ii) Which mathematical concept is used in this question?

(iii) By writing a slogan on the poster, which value is depicted by Ankush? [4 MARKS]

**Q.**The base BC of a triangle ABC is bisected at the point ( a, b ) and the equation of the sides AB and AC are respectively ax + by = 1 and bx + at = 1 equation of the median through A is

**Q.**

Construct rhombuses ABCD with following data .

AB=5cm, ‹60degre

**Q.**Find the value of x in each figure.

- 65∘
- 70∘
- 105∘

**Q.**

What are the properties of a right triangle?

**Q.**

Diagonals do not bisect each other in

Square

Rectangle

Rhombus

Kite

**Q.**

If $PQRS$ is a parallelogram, then $\angle P\u2013\angle R$ is equal to

$60\xb0$

$90\xb0$

$80\xb0$

$0\xb0$

**Q.**Which of these is not a property of rectangle?

- Opposite sides are equal.
- The diagonals are of equal length and intersect perpendicularly.
- Adjacent sides are perpendicular to each other.
- The diagonals are of equal length and bisect each other.

**Q.**Steps for the construction of a rectangle ABCD whose adjacent sides are of lengths 5 cm and 3.5 cm are given below.

Choose the correct order.

1. Draw a line segment BC of length 5 cm.

2.Draw an angle 90° at one of the point A or D and join both points by a line segment AD of length 5 cm.

3.Cut AB and CD of length 3.5 cm from BX and CY, respectively.

4. Generate an angle of 90° at points B and C of the line segment BC and plot the parallel lines BX and CY at these points.

- 1, 2, 3, 4
- 1, 4, 3, 2
- 1, 3, 2, 4
- 1, 4, 2, 3

**Q.**

Median of a triangle divides the opposite side as well as angle of the vertex from where it is drawn.

True

False