Tag: properties of parallel lines and their transversal

Quizzes (2) Questions (42)

Questions Related to properties of parallel lines and their transversal

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

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

  1. $\displaystyle 120cm^{2}$
  2. $\displaystyle 125cm^{2}$
  3. $\displaystyle 150cm^{2}$
  4. $\displaystyle 200cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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


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

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

  1. 3 : 5

  2. 16 : 81

  3. 4 : 9

  4. 2 : 3
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $\displaystyle 60^{\circ}$
  2. $\displaystyle 50^{\circ}$
  3. $\displaystyle 40^{\circ}$
  4. $\displaystyle 80^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\triangle ABC$
$\angle A+\angle B+\angle C=180^{\circ}$
$80^{\circ}+60^{\circ}+\angle C=180^{\circ}$
$\angle C=180^{\circ}-140^{\circ}=40^{\circ}$
$\therefore \angle P=40^{\circ}$

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

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

  1. $\displaystyle 60^{\circ}$
  2. $\displaystyle 70^{\circ}$
  3. $\displaystyle 50^{\circ}$
  4. $\displaystyle 100^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since triangle ABC and DEF are similar 

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

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

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

  1. $10\ cm$
  2. $8\ cm$
  3. $6\ cm$
  4. $4\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

  1. $\displaystyle 83^{\circ}$
  2. $\displaystyle 42^{\circ}$
  3. $\displaystyle 65^{\circ}$
  4. $\displaystyle 97^{\circ}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\triangle ABC$
$\angle A+\angle B+\angle C=180^\circ$
$32^\circ+\angle B+65=180^\circ$
$\angle B=180^\circ-97^\circ$
$\angle B=83^\circ$

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

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

  1. $\displaystyle 40^{\circ}$
  2. $\displaystyle 60^{\circ}$
  3. $\displaystyle 70^{\circ}$
  4. $\displaystyle 110^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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}$
$\angle L+\angle M+\angle N=180^{\circ}$
$60^{\circ}+50^{\circ}+\angle N=180^{\circ}$
$\angle N=180^{\circ}-110^{\circ}$
$\angle N=70^{\circ}$
$\therefore \angle R=70^{\circ}$

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

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

  1. 9.0 cm

  2. 7 cm

  3. 49 cm

  4. 41 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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

  1. $2 : 3$
  2. $4 : 9$
  3. $16 : 81$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

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

  1. $10\ cm$
  2. $8\ cm$
  3. $6\ cm$
  4. $4\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P _1=AB+BC+AC=60  cm$

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