Tag: similarity of triangles

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Questions Related to similarity of triangles

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

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

  1. Differ

  2. Are same

  3. Do not siffer

  4. Angles also differ
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $\dfrac{16} {81}$
  2. $\dfrac{34} {81}$
  3. $\dfrac{81} {16}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 } $

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

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

  1. $\dfrac{9}{4}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{3}{2}$
  4. $\dfrac{2}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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


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


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

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

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

  1. $9$
  2. $3$
  3. $\dfrac{1}{3}$
  4. $\dfrac{1}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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, $\Delta ABC \sim \Delta PQR$

$\therefore \dfrac{ar (\Delta PQR)}{ar (\Delta ABC)} = \dfrac{PR^2}{AC^2} = \dfrac{QR^2}{BC^2} = \dfrac{9}{1} =9 \ \ \ ..........  \left [ \therefore \dfrac{QR}{BC} = \dfrac{3}{1} \right ]$
Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

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

  1. True

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

In similar triangles, the ratio of corresponding medians is equal to the ratio of corresponding sides. Thus, CM/RN = AB/PQ is a true statement.

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

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

  1. True

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

In square ABCD, angle BAC = 45 degrees. The bisector of BAC makes angles of 22.5 degrees. Through geometric properties and angle chasing, it can be shown that triangles ACY and ABX are similar.