Tag: maths

Questions Related to maths

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. $\displaystyle 100^{\circ}$

Show answer
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. $4\ cm$

Show answer
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. $\displaystyle 97^{\circ}$

Show answer
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. $\displaystyle 110^{\circ}$

Show answer
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

Show answer
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

Show answer
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. $4\ cm$

Show answer
Correct Option: A
Explanation:

$P _1=AB+BC+AC=60  cm$

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

SAS criterion is true when two sides  and the included angle is congruent with the when two sides  and the included angle of the other triangle are equal. The included angle means

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. The side between two sides

  2. The angle not between two sides

  3. The line between two sides

  4. The angle between two sides

Show answer
Correct Option: D
Explanation:

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Therefore, D is the correct answer.

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

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. AAA similarity criterion

  2. SAS similarity criterion

  3. SSS similarity criterion

  4. All of the above

Show answer
Correct Option: A
Explanation:

If the corresponding angles are equal then the triangles are similar by $AAA$ similarity criteria.

Option $A$ is correct.

If $\Delta {ABC} \sim \Delta PQR, \angle{B} = \angle{Q}$ is said to be ________ similarity of postulate.

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. SAS similarity postulate

  2. AAA similarity postulate

  3. SSS similarity postulate

  4. AAS similarity postulate

Show answer
Correct Option: A
Explanation:

$\Delta {ABC} \sim \Delta PQR, \angle{B} = \angle{Q}$ is said to be SAS similarity of postulate.
Because, SAS Similarity Postulate states, "If an angle of one triangle is congruent to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar."