Construction of special quadrilaterals - class-IX
construction of special quadrilaterals
Questions
A square with side given can be constructed by using the property of its diagonals.
- True
- False
Can we construct a rhombus $ABCD$ with $AB=4\ cm$? Its diagonal intersect at the point $O$ and $\angle OAB = 60^0$.
- Yes
- No
- Sometimes yes
- Can't say
We cannot construct a square if:
- a side is given
- a diagonal is given
- one angle is $90^0$
- None of these
When given a square, the construction of an angle bisector at any vertex will create the diagonal of the square.
- True
- False
You are given the length of a diagonal of a rhombus and one of the angles of the rhombus. Which property of the rhombus will be used in the construction of this rhombus?
- The lengths of the sides of a rhombus are equal.
- The angles of a rhombus are $90^\circ$
- Diagonal of a rhombus bisects the opposite angles.
- Diagonals of a rhombus are perpendicular bisectors of each other.
If we have to construct a square $PQRS$ whose diagonal is $8 \sqrt 2$ cm then its side is equal to ?
- $8$ cm
- $4\sqrt2$ cm
- $4$ cm
- $8\sqrt2$ cm
State the following statement is True or False
The side of a square is $\sqrt2$ times the diagonal of a square
- True
- False
State the following statement is True or False
We cannot construct the square if only diagonal is given
- True
- False
Which of the following statements is true for a rhombus?
- It has only two pair of equal sides.
- Two of its angles are at right angles.
- Its diagonals bisect each other at right angles.
- It is always a square.
What would be the length of side $BC$ in Square $ABCD$ if the diagonal of the square given is $10$ cm?
- $5$ cm
- $5\sqrt2$ cm
- $10$ cm
- $10\sqrt2$ cm
If one diagonal of a square is the portion of the line $\frac { x }{ a } +\frac { y }{ b } =1$ intercepted by the axes, then the extremities of the other diagonal of the square are
- $\left( \frac { a+b }{ 2 } ,\frac { a+b }{ 2 } \right) $
- $\left( \frac { a-b }{ 2 } ,\frac { a+b }{ 2 } \right) $
- $\left( \frac { a-b }{ 2 } ,\frac { b-a }{ 2 } \right) $
- $\left( \frac { a+b }{ 2 } ,\frac { b-a }{ 2 } \right) $
The diagonal of rectangle $ABCD$ intersect each other at $O$. If $\angle AOB = 30^0$, then we can construct a rectangle if _________ is given.
- diagonal
- one side
- both sides
- $\angle COD$
We can construct a parallelogram if:
- its adjacent sides and a diagonal are given
- its diagonal and one angle are given
- its four angles and a side are given
- None of these are given
Construct a parallelogram $ABCD$ with $AB=24$ cm and $AD=16$ cm. The distance between AB and DC is $10$ cm. Find the area of parallelogram $ABCD$ in sq. cm.
- $240$
- $235$
- $270$
- None of these
Construct a parallelogram $ABCD$, with adjacent sides $AB=4$ cm, $BC = 5$ cm and height corresponding to (base) $BC = 3.5$ cm. Find the area of parallelogram ABCD in sq. cm.
- $21.5$
- $14.5$
- $17.5$
- None of these
State whether the following statement is True or False.
The length of diagonal of rectangle is more than any side of rectangle.
- True
- False
Construct a rectangle $ABCD$, where $AB=10$ cm and $BC=8$ cm.Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) Join these cuts with a line $CD$ and rectangle $ABCD$ is formed
2) Draw a straight line $AB$ of length $10$ cm
3) Draw perpendicular lines at $A$ and $B$ using protractor.
4) Using compass cut arc at the perpendicular from $A$ and $B$ of lengths $8$ cm
- $2,4,3,1$
- $2,3,4,1$
- $3,2,4,1$
- $3,4,2,1$
Let $ABCD$ be a square in which $A$ lies on the positive y-axis and $B$ lies on the positive x-axis. If $D$ is the point $(12, 17)$ the coordinates of $C$ are.
- $(17, 12)$
- $(17, 5)$
- $(14, 16)$
- $(15, 3)$
Construct a parallelogram $ABCD$ with $AB=24$ cm and $AD=16$ cm. The distance between AB and DC is $10$ cm. Find the distance between AD and BC.
- $25 $ cm
- $15 $ cm
- $13 $ cm
- None of these