Tag: properties of parallel lines and their transversal

Questions Related to properties of parallel lines and their transversal

If $\displaystyle \triangle ABC\sim \triangle DEF$ BC=4 cm, EF=5 cm and ar $\displaystyle \left ( \triangle ABC \right )=80cm2$,the ar$\displaystyle \left ( \triangle DEF \right )$ is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $\displaystyle 120cm^{2}$

  2. $\displaystyle 125cm^{2}$

  3. $\displaystyle 150cm^{2}$

  4. $\displaystyle 200cm^{2}$

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Correct Option: B
Explanation:

If two triangles are equals than the ratio of their square is equal to the ratio of their corresponding sides.

$\therefore \dfrac{arc(\triangle ABC)}{arc(\triangle DEF)}=\dfrac{BC^2}{EF^2}$
$\Rightarrow \dfrac{80}{arc(\triangle DEF)}=\dfrac{16}{25}$
$\Rightarrow arc(\triangle DEF)=\dfrac{80\times 25}{16}=125 cm^2$


If the ratio of the corresponding sides of two similar triangles is 2:3 then the ratio of their corresponding altitude is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. 3 : 5

  2. 16 : 81

  3. 4 : 9

  4. 2 : 3

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Correct Option: D
Explanation:

If two triangles are similar ,then the ratio of their corresponding sides and altitude are also same. Therefore the ratio of the altitude is 2:3.

If $\displaystyle \triangle ABC\cong \triangle RQP,\angle A=80^{\circ},\angle B=60^{\circ}$, then the value of $\displaystyle \angle P$ is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $\displaystyle 60^{\circ}$

  2. $\displaystyle 50^{\circ}$

  3. $\displaystyle 40^{\circ}$

  4. $\displaystyle 80^{\circ}$

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Correct Option: C
Explanation:

If two triangles are equal then their corresponding angle are also equal

$\therefore \angle A=\angle R,$$\angle B=\angle Q$ and$ \angle C=\angle P$
In $\triangle ABC$
$\angle A+\angle B+\angle C=180^{\circ}$
$80^{\circ}+60^{\circ}+\angle C=180^{\circ}$
$\angle C=180^{\circ}-140^{\circ}=40^{\circ}$
$\therefore \angle P=40^{\circ}$

If ABC and DEF are similar triangles such that $\displaystyle \angle A=47^{\circ}$ and $\displaystyle \angle B=83^{\circ}$ then $\displaystyle \angle F$ is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $\displaystyle 60^{\circ}$

  2. $\displaystyle 70^{\circ}$

  3. $\displaystyle 50^{\circ}$

  4. $\displaystyle 100^{\circ}$

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Correct Option: C
Explanation:

Since triangle ABC and DEF are similar 

$\therefore \angle A=\angle D,\angle B=\angle E   and  \angle  C=\angle F$
In $\triangle ABC$
$\angle A+\angle B+\angle C=180^\circ$
$47^\circ+83^\circ+\angle C=180^\circ$
$\angle C=180^\circ-130^\circ$
$\angle C=50^\circ$
$\therefore \angle F=50^\circ$

The perimeters of two similar triangles ABC and LMN are 60 cm and 48 cm respectively If LM=8 cm, the length of AB is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $10\ cm$

  2. $8\ cm$

  3. $6\ cm$

  4. $4\ cm$

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Correct Option: A
Explanation:

If two triangles are similar then the ratio of their perimeter is equal to the ratio of their corresponding sides.

$\therefore \dfrac{perimeter\ ABC}{perimeter\ LMN}=\dfrac{AB}{LM}$
$\Rightarrow \dfrac{60}{48}=\dfrac{AB}{8}$
$\Rightarrow AB=\dfrac{60\times 8}{48}=10 cm$

If $\displaystyle \triangle ABC$ and $\displaystyle \triangle PQR$ are similar triangles such that $\displaystyle \angle A=32^{\circ}$ and $\displaystyle \angle R=65^{\circ}$ then $\displaystyle \angle B$ is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $\displaystyle 83^{\circ}$

  2. $\displaystyle 42^{\circ}$

  3. $\displaystyle 65^{\circ}$

  4. $\displaystyle 97^{\circ}$

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Correct Option: A
Explanation:

Since triangle ABC anD PQR are similar 

$\therefore \angle A=\angle P,\angle B=\angle Q   and  \angle  C=\angle R=65^\circ$
In $\triangle ABC$
$\angle A+\angle B+\angle C=180^\circ$
$32^\circ+\angle B+65=180^\circ$
$\angle B=180^\circ-97^\circ$
$\angle B=83^\circ$

In $\displaystyle \triangle LMN,\triangle L=60^{\circ},\angle M=50^{\circ}$ If $\displaystyle \angle LMN\sim \triangle PQR$ then the value of $\displaystyle \angle R$ is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $\displaystyle 40^{\circ}$

  2. $\displaystyle 60^{\circ}$

  3. $\displaystyle 70^{\circ}$

  4. $\displaystyle 110^{\circ}$

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Correct Option: C
Explanation:

$\because \triangle LMN=\triangle PQR$ then

$\angle L=\angle P$,$\angle M=Q$,$\angle N=\angle R$
In $\triangle LMN$$\angle L=60^{\circ},\angle M=50^{\circ}$
$\angle L+\angle M+\angle N=180^{\circ}$
$60^{\circ}+50^{\circ}+\angle N=180^{\circ}$
$\angle N=180^{\circ}-110^{\circ}$
$\angle N=70^{\circ}$
$\therefore \angle R=70^{\circ}$

The area of two similar triangles ABC and PQR are 25 $\displaystyle cm^{2}$ and $\displaystyle 49cm^{2}$ If QR=9.8 cm then BC is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. 9.0 cm

  2. 7 cm

  3. 49 cm

  4. 41 cm

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Correct Option: B
Explanation:

If two triangles are equals than the ratio of their square is equal to the ratio of their corresponding sides.

$\therefore \dfrac{arc(\triangle ABC)}{arc(\triangle PQR)}=\dfrac{BC^2}{QR^2}$
$\Rightarrow \dfrac{25}{49}=\dfrac{BC^2}{(9.8)^2}$
$\Rightarrow \dfrac{5}{7}=\dfrac{BC}{9.8}$
$\Rightarrow BC=\dfrac{9.8\times 5}{7}=7.0 cm^2$

If the ratio of the corresponding sides of the two similar triangles is 2 : 3 then the ratio of their corresponding attitudes is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $2 : 3$

  2. $4 : 9$

  3. $16 : 81$

  4. none of these

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Correct Option: A
Explanation:

If two triangles are same than their sides and corresponding attitudes are also same then the ratio of the corresponding altitude is 2:3. 

The perimeters of two similar triangles ABC and PQR are 60 cm and 48 cm respectively If PQ=8 cm length of AB is

maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

  1. $10\ cm$

  2. $8\ cm$

  3. $6\ cm$

  4. $4\ cm$

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Correct Option: A
Explanation:

$P _1=AB+BC+AC=60  cm$

$P _2=PQ+QR+RP=48  cm$
PQ=8 cm
$\dfrac{P _1}{P _2}=\dfrac{AB}{PQ}$
$\Rightarrow \dfrac{60}{48}=\dfrac{AB}{8}$
$\Rightarrow AB=\dfrac{60\times 8}{48}=10 cm$