Tag: how to check for similarity in triangles?

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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

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

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

  1. AAA similarity criterion

  2. SAS similarity criterion

  3. SSS similarity criterion

  4. All of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Option $A$ is correct.

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

  1. SAS similarity postulate

  2. AAA similarity postulate

  3. SSS similarity postulate

  4. AAS similarity postulate
Reveal answer Fill a bubble to check yourself
A Correct answer
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."

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

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

  1. SSS Similarity

  2. AAA similarity

  3. Basic proportionality theorem
  4. $A$ and $C$ are correct
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

Goldfish are sold at Rs.15 each. The rectangular coordinate graph showing the cost of 1 to 12 goldfish is:

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
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 } $

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

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.

  1. $RQP$
  2. $PQR$
  3. $RPQ$
  4. $QPR$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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.

  1. True

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

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

$ABC$ 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

  1. $2:1$
  2. $1:2$
  3. $4:1$
  4. $1:4$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.