Tag: properties of parallel lines and their transversal

Questions Related to properties of parallel lines and their transversal

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."

When we construct a triangle similar to a given triangle as per given scale factor, we construct on the basis of ...........

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. SSS Similarity

  2. AAA similarity

  3. Basic proportionality theorem

  4. $A$ and $C$ are correct

Show answer
Correct Option: A
Explanation:

As we consider only sides, therefore, SSS similarity is used.
Option A is correct.  

Goldfish are sold at Rs.15 each. The rectangular coordinate graph showing the cost of 1 to 12 goldfish 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. a straight line segment

  2. a set of horizontal parallel line segments

  3. a set of vertical parallel line segments

  4. a finite set of distinct points

  5. a straight line

Show answer
Correct Option: D
Explanation:

$\angle MAB=\angle PAO\longrightarrow (1),\hspace{1mm} O\hspace{1mm} be\hspace{1mm} center\ \angle AMB=90°=\angle AOP\ (1)\Longrightarrow 90°-\angle MAB=90°-\angle PAO\ \angle MBA=\angle APO$

By AAA property,
$\triangle APO\sim \triangle ABM\ \cfrac { \bar { AP }  }{ \bar { AB }  } =\cfrac { \bar { AO }  }{ \bar { AM }  } \ \therefore \bar { AP } \cdot \bar { AM } =\bar { AO } \cdot \bar { AB } $

For $\triangle ABC$ and $\triangle PQR$, if $m\angle A=m\angle R $ and $m\angle C=m\angle Q$, then $ABC \longleftrightarrow $_________ is a similarity.

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. $RQP$

  2. $PQR$

  3. $RPQ$

  4. $QPR$

Show answer
Correct Option: C
Explanation:

For $\triangle ABC $ and $\triangle PQR$,
$m\angle A = m\angle R$
$m\angle C= m\angle Q$
$\therefore $ by AA criteria for similarity 

$ABC \longleftrightarrow RPQ $ is a similarity.

Say true or false.

If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then 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. True

  2. False

Show answer
Correct Option: A
Explanation:

If two angles of a triangle is equal to two angles of another triangle, then the third angle of both triangles will be equal.
$\therefore$By AAA Theorem of Similarity, the two triangles are similar.

In $\triangle DEF$ &$ \triangle PQR,\ m \angle R$  & _____, then both 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. $\dfrac{DE}{PQ}=\dfrac{EF}{QR}$

  2. $\dfrac{DE}{PQ}=\dfrac{DF}{PR}$

  3. $\dfrac{DE}{PR}=\dfrac{DF}{RQ}$

  4. $\dfrac{DE}{QR}=\dfrac{EF}{PR}$

Show answer
Correct Option: A

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid point of $BC$. Ratio of the areas of triangle $ABC$ and $BDE$ 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. $2:1$

  2. $1:2$

  3. $4:1$

  4. $1:4$

Show answer
Correct Option: C
Explanation:

$\triangle ABC \sim \triangle BDE$                            (both are equilateral triangles)


$\Rightarrow \triangle ABC : \triangle BDE = AB^2 : BD^2$

                                          $= AB^2 :  (\dfrac{1}{2} BC)^{2} $
                                          
                                          $ = AB^2 : \dfrac{1}{4} BC^2 $

                                          $= 4 : 1$           $(\because AB = BC)$
Hence proof.

In $ \triangle ABC, $ If $\angle ADE = \angle B,$ then  $ \Delta ADE ~ \Delta ABC$ 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. True

  2. False

Show answer
Correct Option: A