Tag: maths

Questions Related to maths

Two quadrilaterals, a square and a rectangle are not similar as they ......... in shape as well as size.

maths properties of parallel lines and their transversal introduction to shapes similarity of triangles introduction to similar triangles

  1. Differ

  2. Are same

  3. Do not siffer

  4. Angles also differ

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Correct Option: A
Explanation:

When two quadrilaterals having corresponding angles equal but their corresponding sides are not equal, such figures are not similar.
Therefore, A is the correct answer.

Ratio of two corresponding sides of two similar triangles is $4:9$. Then ratio of their area is ___.

maths properties of parallel lines and their transversal introduction to shapes similarity of triangles introduction to similar triangles

  1. $\dfrac{16} {81}$

  2. $\dfrac{34} {81}$

  3. $\dfrac{81} {16}$

  4. $None\ of\ these$

Show answer
Correct Option: A
Explanation:

Ratio of areas of two similar triangles is equal to the squares of the ratio of their sides.

Ratio of sides $=\dfrac{4}{9}$
Ratio of areas $=\left( \dfrac { 4 }{ 9 }  \right) ^{ 2 }=\dfrac { 16 }{ 81 } $

$\triangle PQR \sim \triangle XYZ, \dfrac{XY}{PQ}=\dfrac{3}{2}$ then $\dfrac{Area\ of\ \triangle PQR}{Area\ of\ \triangle XYZ}=$____.

maths properties of parallel lines and their transversal introduction to shapes similarity of triangles introduction to similar triangles

  1. $\dfrac{9}{4}$

  2. $\dfrac{4}{9}$

  3. $\dfrac{3}{2}$

  4. $\dfrac{2}{3}$

Show answer
Correct Option: B
Explanation:

$\dfrac{{XY}}{{PQ}} = \dfrac{3}{2}$


$ \Rightarrow \dfrac{{PQ}}{{XY}} = \dfrac{2}{3}$


Now,  $\dfrac{{Area{\rm{ of  }}\Delta {\rm{PQR}}}}{{Area{\rm{ of  }}\Delta {\rm{XYZ}}}} = {\left( {\dfrac{2}{3}} \right)^2} = \dfrac{4}{9}$

ABCD is a tetrahedron and O is any point. If the lines joining O to the vertices meet the opposite at P, Q, R and S, then $\frac{OP}{AP}+\frac{OQ}{BQ}+\frac{OR}{CR}+\frac{OS}{DS}=2$.

maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. True

  2. False

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Correct Option: B

It is given that $\Delta ABC \sim \Delta PQR$ with $\dfrac{BC}{QR} = \dfrac{1}{3}$. Then $\dfrac{ar (\Delta PQR)}{ar (\Delta ABC)}$ is equal to

maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. $9$

  2. $3$

  3. $\dfrac{1}{3}$

  4. $\dfrac{1}{9}$

Show answer
Correct Option: A
Explanation:
 If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Since, $\Delta ABC \sim \Delta PQR$

$\therefore \dfrac{ar (\Delta PQR)}{ar (\Delta ABC)} = \dfrac{PR^2}{AC^2} = \dfrac{QR^2}{BC^2} = \dfrac{9}{1} =9 \ \ \ ..........  \left [ \therefore \dfrac{QR}{BC} = \dfrac{3}{1} \right ]$

$CM$ and $RN$ are respectively the medians of $\triangle {ABC}$ and $\triangle{PQR}$. If $\triangle {ABC}\sim \triangle{PQR}$, then
  $\cfrac{CM}{RN}=\cfrac{AB}{PQ}$

maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. True

  2. False

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Correct Option: A

In a square $ABCD$, the bisector of the angle $BAC$ cut $BD$ at $X$ and $BC$ at $Y$ then triangles $ACY, ABX$ are similar.

maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. True

  2. False

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Correct Option: A

Assume that, $\Delta RST \sim \Delta XYZ$. Complete the following statement.


$\displaystyle \frac{RT}{XY} = \frac{- -}{YZ}, \frac{RS}{XY} = \frac{ST}{- -}, \frac{XY}{ - -} = \frac{YZ}{ST}$

maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. ST, YZ, RT

  2. ST, YZ, RS

  3. YT, YS, RZ

  4. ST, YZ, RZ

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Correct Option: B
It is given that $\triangle FED\sim \triangle STU$. Is it true to say that $\cfrac{DE}{UT}=\cfrac{EF}{TS}$? 
maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. Yes

  2. No

  3. Cannot say

  4. None

Show answer
Correct Option: B
Explanation:

$\triangle FED \sim \triangle STU$
The corresponding sides of both the triangles are $F\leftrightarrow S$, $E\leftrightarrow T$, $D\leftrightarrow  U$. With this correspondence,
$\cfrac{EF}{ST}=\cfrac{DE}{TU}$

Consider the following statements:
(1) If three sides of triangle are equal to three sides of another triangle, then the triangles are congruent.
(2) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.

Of these statements,

maths congruence introduction to shapes similarity of triangles introduction to similar triangles

  1. $(1)$ is correct and $(2)$ is false

  2. Both $(1)$ and $(2)$ are false

  3. Both $(1)$ and $(2)$ are correct

  4. $(1)$ is false and $(2)$ is correct

Show answer
Correct Option: A
Explanation:

If three sides of triangle are equal to other three sides of the triangle, then the two triangles are congruent by SSS rule.

If three angles of the triangle are equal to other three sides of the triangle, then the two triangles are similar by AAA rule but not congruent.