Tag: when lines join

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Questions Related to when lines join

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

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

  1. $\displaystyle \angle B$
  2. $\displaystyle \angle A$
  3. $\displaystyle \angle D$

  4. Depends on the naming of the trapezium
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. Square

  2. Trapezium

  3. Rhombus

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

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 ) $[P _{1}...P _{n}]$

  1. $2-\sqrt {3}$
  2. $3-2\sqrt {2}$
  3. $\sqrt {3}-\sqrt {2}$
  4. $2(\sqrt {3}-\sqrt {2})$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ratio of areas of triangles formed by diagonals in a trapezium is the square of the ratio of the parallel sides. The calculation leads to the provided value.

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

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 $AC=........\ .$

  1. $4$
  2. $12$
  3. $13$
  4. $9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a trapezium, the diagonals intersect such that triangles ADP and BCP are similar. Using the ratio of segments PA/PC = PD/PB, we find PC = (PA * PB) / PD = (5 * 7.2) / 9 = 4. Then AC = PA + PC = 5 + 4 = 9.

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

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 __

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a right-angled trapezium with an inscribed circle, the height (the right-angled leg) is indeed the geometric mean of the bases, and the harmonic mean relationship is a known property.

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

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

  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. $(p^{2}+q^{2})\sin\theta/p\sin\theta+q\cos\theta$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the properties of a right-angled trapezium where CD is perpendicular to BC, we can use trigonometry in the triangles formed by the diagonals. By expressing the lengths in terms of theta, p, and q, the derived expression matches option A.