Tag: similarity of triangles

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Questions Related to similarity of triangles

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

Assume that, $\Delta RST \sim \Delta XYZ$. Complete the following statement.


$\displaystyle \frac{RT}{XY} = \frac{- -}{YZ}, \frac{RS}{XY} = \frac{ST}{- -}, \frac{XY}{ - -} = \frac{YZ}{ST}$

  1. ST, YZ, RT

  2. ST, YZ, RS

  3. YT, YS, RZ

  4. ST, YZ, RZ
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given triangle RST similar to triangle XYZ, the ratios of corresponding sides are equal: RS/XY = ST/YZ = RT/XZ. The provided option B correctly completes the ratios.

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles
It is given that $\triangle FED\sim \triangle STU$. Is it true to say that $\cfrac{DE}{UT}=\cfrac{EF}{TS}$? 

  1. Yes

  2. No

  3. Cannot say

  4. None
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\triangle FED \sim \triangle STU$
The corresponding sides of both the triangles are $F\leftrightarrow S$, $E\leftrightarrow T$, $D\leftrightarrow  U$. With this correspondence,
$\cfrac{EF}{ST}=\cfrac{DE}{TU}$

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

Consider the following statements:
(1) If three sides of triangle are equal to three sides of another triangle, then the triangles are congruent.
(2) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.

Of these statements,

  1. $(1)$ is correct and $(2)$ is false
  2. Both $(1)$ and $(2)$ are false
  3. Both $(1)$ and $(2)$ are correct
  4. $(1)$ is false and $(2)$ is correct
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If three sides of triangle are equal to other three sides of the triangle, then the two triangles are congruent by SSS rule.

If three angles of the triangle are equal to other three sides of the triangle, then the two triangles are similar by AAA rule but not congruent.

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

If in trianges $ABC$ and $DEF$, $\cfrac{AB}{DE}=\cfrac{BC}{FD}$, then they will be similar, when:

  1. $\angle B=\angle E$
  2. $\angle A=\angle D$
  3. $\angle B=\angle D$
  4. $\angle A=\angle F$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In $\triangle ABC$ and $\triangle DEF$,
$\dfrac{AB}{DE} = \dfrac{BC}{FD}$ (Given)

The angle between these sides are $\angle B$ and $\angle D$. Thus, If the containing angles are equal. The triangles will be similar..

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

In $\triangle PQR,$ $PQ=4$ cm, $QR=3$ cm, and $RP=3.5$ cm. $\triangle DEF$ is similar to $\triangle PQR.$ If $EF=9$ cm, then what is the perimeter of $\triangle DEF: ?$

  1. $10.5$ cm
  2. $21$ cm
  3. $31.5$ cm

  4. Cannot be determined as data is insufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$PQ = 4, QR = 3$ and $RP = 3.5$
Also, $EF = 9$
Now, perimeter of $\triangle PQR = PQ + QR + RP = 4 + 3 + 3.5 = 10.5$
Given, $\triangle DEF \sim \triangle PQR$
$\dfrac{EF}{QR} = \dfrac{Perimeter(\triangle DEF)}{Perimeter(\triangle PQR)}$
$\dfrac{9}{3} = \dfrac{Perimeter(\triangle DEF)}{10.5}$
Perimeter $(\triangle DEF) = 31.5$ cm

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

The perimeter of two similar triangles are $24$ cm and $16$ cm, respectively. If one side of the first triangle is $10$ cm, then the corresponding side of the second triangle is

  1. $9$ cm
  2. $\dfrac{20}3$ cm
  3. $\dfrac{16}3$ cm
  4. $5$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
In similar triangles, ratio of the sides is equal to the ratio of the perimeters.
Thus, $\dfrac{p _1}{p _2} = \dfrac{s _1}{s _2}$
$\dfrac{24}{16} = \dfrac{10}{s _2}$
$s _2 = \dfrac{20}{3}$
Thus, side of the other triangle is $\dfrac{20}{3}$ cm.
Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

In a $\triangle ABC$, $BC=AB$ and $\angle B={ 80 }^{ 0 }$. Then $\angle A$ is equal to?

  1. ${ 80 }^{ 0 }$
  2. ${ 40 }^{ 0 }$
  3. ${ 50 }^{ 0 }$
  4. ${ 100 }^{ 0 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given: $BC = AB$, $\angle B = 80^{\circ}$
Since, $BC = AB$
$\angle A = \angle C = x$ (Angles opposite to equal sides are equal)
Sum of angles of a triangle = 180
$\angle A + \angle B + \angle C = 180$
$x + 80 + x = 180$
$2x = 100$
$x = 50^{\circ}$
Thus, $\angle A = 50^{\circ}$

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

The area of two similar triangles $\displaystyle \Delta ABC$ and $\displaystyle \Delta DEF$ are 144 $\displaystyle cm^{2}$ and 81 $\displaystyle cm^{2}$ respectively If the longest side of larger $\displaystyle \Delta ABC$ be 36 cm then the longest side of the smaller triangle $\displaystyle \Delta DEF$ is

  1. 20 cm

  2. 26 cm

  3. 27 cm

  4. 30 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In similar triangle ABC & DBF
$\frac{AB}{De}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{ratio ofArea of triangleABC}{ratio ofArea of triangleDEF}$ 
THEN $\frac{9}{12}=\frac{x}{36}$  (where x is longest side of the smaller triangle )
So x=27 cm

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

The perimeters of two similar triangles are $25\;cm$ and $15\;cm$ respectively. If one side of first triangle is $9\;cm$, then the corresponding side of the other triangle is

  1. $6.2\;cm$
  2. $3.4\;cm$
  3. $5.4\;cm$
  4. $8.4\;cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$The\quad perimeter\quad of\quad triangle\quad is\quad 25cm\quad and\quad 15cm.\ The\quad ratio\quad of\quad Perimeter\quad of\quad triangle\quad is\quad 25:15=5:3\ The\quad first\quad side\quad is\quad 9cm\quad ,let\quad the\quad other\quad side=x\ Hence,\quad \dfrac { 9 }{ x } =\dfrac { 5 }{ 3\  } \ \Rightarrow x=\dfrac { 3\times 9 }{ 5 } =\dfrac { 27 }{ 5 } =5.4\quad cm$

Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

If area $(\Delta ABC)=36 cm^2, area (\Delta DEF)=64 cm^2$ and $DE=6.4 cm$. Find AB if $\Delta ABC\sim \Delta DEF$

  1. $3.6$ cm
  2. $7.2$ cm
  3. $4.8 $cm

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In similar triangles, $\dfrac {area\Delta ABC}{area \Delta DEF}=\dfrac {AB^2}{DE^2}=\dfrac {36}{64}$


$\Rightarrow \dfrac {AB}{6.4}=\dfrac {3}{4}\Rightarrow AB=4.8$.