Construction of a Quadrilateral When Other Special Properties Are Known

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.

1. circumcenter
2. orthocenter
3. centroid
4. incenter

Q.

Diagonals of a parallelogram are perpendicular to each other.

Is this statement true?

Give reason for your answer.

1. True
2. False

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

1. 3
2. 4
3. 1
4. 2

Q. Steps for the construction of a parallelogram ABCD with sides AB = 4 cm and AD = 5 cm and angle A $={60}^{\circ }$ are given below.

Choose the correct order.

1. Construct a line segment AB = 4 cm and construct a ${60}^{\circ }$ 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. 1, 4, 3, 2
2. 1, 2, 3, 4
3. 1, 3, 2, 4
4. 1, 4, 2, 3

Q.

The adjacent sides of a rectangle are:

1. Coincident

2. Perpendicular

3. Parallel

4. 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, $\angle A={60}^{\circ }$ and $\angle B={85}^{\circ }$ [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$°$, 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, $\angle$ ABC = ${110}^{\circ }$, $\angle$ DAC = ${15}^{\circ }$, $\angle$ CAB=${25}^{\circ }$, AB = 5cm, CD = 7cm. Can we construct this parallelogram?

1. With ADC, yes

2. No, it is impossible

3. Yes, of course

4. 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. 1, 2, 4, 3, 5
2. 1, 2, 3, 4, 5
3. 1, 2, 5, 4, 3
4. 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

1. Incentre
2. Orthocentre
3. Centroid
4. Circumcentre

Q.

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

1. centre

2. vertex

3. random point inside the triangle

4. 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 $\angle A=(5x+7{)}^{\circ }$ and $\angle B=(3x-3{)}^{\circ }$, 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.

1. ${65}^{\circ }$
2. ${70}^{\circ }$
3. ${105}^{\circ }$

Q.

What are the properties of a right triangle?

Q.

Diagonals do not bisect each other in

1. Square

2. Rectangle

3. Rhombus

4. Kite

Q.

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

1. $60°$

2. $90°$

3. $80°$

4. $0°$

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

1. Opposite sides are equal.
2. The diagonals are of equal length and intersect perpendicularly.
3. Adjacent sides are perpendicular to each other.
4. 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. 1, 2, 3, 4
2. 1, 4, 3, 2
3. 1, 3, 2, 4
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.

1. True

2. False