Tag: congruence

Quizzes (1) Questions (67)

Questions Related to congruence

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


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

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

If the areas of two similar triangles are equal then the triangles :

  1. are congruent

  2. have equal length of corresponding sides

  3. (A) and (B)

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

Triangles are similar if they have the same shape, but not necessarily the same size.   It is same as keeping its basic shape but either "zooming in" or out making the triangle bigger or smaller .

For triangles to be congruent if one triangle slides over the other , rotate them, and flip them over in various ways so they will exactly fit over each other.

So, if the triangles are similar, i.e. they are "zoomed-in" or "zoomed-out" versions of each other, and if they have equal area, then they are congruent, and hence have equal corresponding sides.

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

Sides of two similar triangles are in the ratio of $5 : 11$ then ratio of their areas is 

  1. $25 : 11$
  2. $25 : 121$
  3. $125 : 121$
  4. $121 : 25$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since, ratio of area of two similar traingles = ratio of square of corresponding sides

 ratio of sides = 5 : 11
$\therefore$ ratio of their areas = $(5)^2 : (11)^2 = 25 : 121$

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

Sides of two similar triangles are in the ratio of $4 : 9$ then area of these triangles are in the ratio

  1. $2 : 3$
  2. $4 : 9$
  3. $81 : 16$
  4. $16 : 81$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \because \Delta ABC\sim \Delta DEF$
$\displaystyle \therefore \dfrac{ar\Delta ABC}{ar\Delta DEF}=\dfrac{\left ( 4 \right )^{2}}{\left ( 9 \right )^{2}}=\dfrac{16}{81}=16:81.$