Tag: when lines join

Questions Related to when lines join

If $ABCD$ is an isosceles trapezium $\displaystyle \angle C$ is equal to:

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. $\displaystyle \angle B$

  2. $\displaystyle \angle A$

  3. $\displaystyle \angle D$

  4. Depends on the naming of the trapezium

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Correct Option: D
Explanation:

$Properties\  of \ an \ isosceles\  trapezium:  $

It has a pair of parallel sides.

It has a pair of opposite sides that are congruent.

Both pairs of opposite angles are supplementary, that is they sum to $180°$.

Consecutive angles along both bases are congruent.

Diagonals are congruent.

$\therefore $In an isosceles trapezium the base angles are always equal. Hence, it depends how we name an isosceles trapezium.

The base angles of a issoceles trapezium are .....................

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. unequal

  2. equal

  3. circular

  4. diagonals

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Correct Option: B
Explanation:

If the trapezium is an isosceles trapezoid it has equal angles according to the trapezoid theorem.
Therefore, B is the correct answer.

State true or false:

Every parallelogram is a trapezium.

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. True

  2. False

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Correct Option: B
Explanation:

The pair of opposite sides of a parallelogram are equal and parallel but in the case of the trapezium, this is not true.

A quadrilateral-shaped photo-frame has all sides equal. Which of the following is not a possible shape for the photo-frame.

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. Square

  2. Trapezium

  3. Rhombus

  4. None of these

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Correct Option: B
Explanation:
A trapezium is a quadrilateral having one pair of opposite sides parallel. The other pair of opposite sides are non parallel and equal. Hence , the photo frame can be a square or a rhombus where all the sides are equal. The shape of the photo frame can not be a trapezium.

In trapezium $ABCD$ has $AD$ parallel to $BC,AC$ and $BD$ intersect at $P$. If $\dfrac {[ADP]}{[BCP]}=\dfrac {1}{2}$, find $\dfrac {[ADP]}{[ABCD]}$. (Here the notion $[P _{1}...P _{n}]$ denotes the area of the polygon ) $[P _{1}...P _{n}]$

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. $2-\sqrt {3}$

  2. $3-2\sqrt {2}$

  3. $\sqrt {3}-\sqrt {2}$

  4. $2(\sqrt {3}-\sqrt {2})$

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Correct Option: A

In trapezium $ABCD,\ \overline {AD} \parallel \overline {BC} $ and $\overline {AC} \bigcap  \overline {BD}=\left{P\right}$. If $PD=9,\ PA=5$ and $PB=7.2$ then $AC=........\ .$

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. $4$

  2. $12$

  3. $13$

  4. $9$

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Correct Option: D

Given that a right angled trapezium has an inscribed circle. then " the length of the right angled leg is the Harmonic mean of the lengths of bases. "that  statement is __

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. True

  2. False

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Correct Option: A

$ABCD$ is a trapezium with side $BC$  parallel to $AD$ . If E is midpoint of $AB$ and the line through E parallel to $DC$ meets $AD$ and $BC$ at $X$ and $Y$ respectively . these this relation is  $\left[ {ABCD} \right] = \left[ {XYCD} \right]$ . is ?

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. True

  2. False

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Correct Option: A

If $ABCD$ is a trapezium such that $AB\parallel CD$. Also $CD\bot BC$. If $\angle ADB=\theta, BC=p, CD=q$ then $AB$=?

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. $(p^{2}+q^{2})\cos\theta/p\cos\theta+q\sin\theta$

  2. $(p^{2}+q^{2})\cos\theta/p\sin\theta+q\cos\theta$

  3. $(p^{2}+q^{2})\sin\theta/p\cos\theta+q\sin\theta$

  4. $(p^{2}+q^{2})\sin\theta/p\sin\theta+q\cos\theta$

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Correct Option: A

In the case of trapezium, the ratio of its angles taken in order cannot be 

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. 1:2:3:4

  2. 7:13::2:8

  3. 6:3:4:2

  4. 4:5:2:3

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Correct Option: A