Tag: congruence

Quizzes (1) Questions (67)

Questions Related to congruence

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

Two $\triangle sABC $ and DEF are similar. If $ar(DEF)= 243\ cm^2, ar(ABC)=108\ cm^2$ and $BC= 6\ cm$. Find $EF$.

  1. $9$
  2. $81$
  3. $3$
  4. $72$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given:-
$\triangle{ABC} \simeq \triangle{DEF}$
$ar \left( DEF \right) = 243 {cm}^{2}$
$ar \left( ABC \right) = 108 {cm}^{2}$
$BC = 6 cm$

To Find:- $EF = ?$

As we know that,
$\because \; \triangle{ABC} \simeq \triangle{DEF}$

$\cfrac{ar \left( \triangle{ABC} \right)}{ar \left( \triangle{DEF} \right)} = {\left( \cfrac{AB}{DE} \right)}^{2} = {\left( \cfrac{BC}{EF} \right)}^{2} = {\left( \cfrac{AC}{DF} \right)}^{2}$

$\therefore \; \cfrac{ar \left( \triangle{ABC} \right)}{ar \left( \triangle{DEF} \right)} = {\left( \cfrac{BC}{EF} \right)}^{2}$

$\Rightarrow \; \cfrac{108}{243} = \cfrac{{6}^{2}}{{EF}^{2}}$

$\Rightarrow \; {EF}^{2} = \cfrac{243}{108} \times 36$

$\Rightarrow \; EF = \sqrt{81}$

$\Rightarrow \; EF = 9$

Hence, the correct answer is $9$.
Multiple choice maths congruence introduction to shapes similarity of triangles introduction to similar triangles

STATEMENT - 1 : 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.
STATEMENT - 2 : 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. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 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.

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
Both the statements are correct but $2$ is not the reason for $1$
If two corresponding angles are equal then the third corresponding become also equal , so the triangles are similar.
Option $B$ is correct

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

Is the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians?

  1. True

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

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides, which is also equal to the square of the ratio of their corresponding medians.

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

The areas of two similar triangles $\triangle{ABC}$ and $\triangle{DEF}$ are $144\ cm^{2}$ and $81\ cm^{2}$ respectively. If the longest side of larger $\triangle{ABC}$ be $36\ cm$, then, the largest side of the similar triangle $\triangle{DEF}$ 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

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, the ratio of their sides is the square root of the ratio of their areas, which is sqrt(144/81) = 12/9 = 4/3. Setting up the proportion 36/x = 4/3 yields x = 27 cm for the smaller triangle's corresponding side.

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

The correspondence $ABC\rightarrow PQR$ is a similarity in $\Delta ABC$ and $\Delta PQR$. If the perimeter of $\Delta ABC$ is $24$ and the perimeter of $\Delta PQR$ is $40$, then $AB=PQ=$

  1. $4:3$
  2. $3:4$
  3. $5:3$
  4. $3:5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For similar triangles, the ratio of any pair of corresponding sides is equal to the ratio of their perimeters. Given the perimeter of ABC is 24 and PQR is 40, the ratio is 24/40, which simplifies to 3/5. Thus, the ratio AB/PQ equals 3/5.

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

The ratio of the angles in $\triangle ABC$ is $2 : 3 : 4$. Which one of the following triangles is similar to $\triangle ABC ?$

  1. $ \triangle DEF $ has angles in the ratio $4 : 3 : 2.$
  2. $ \triangle PQR $ has angles in the ratio $1 : 2 : 3.$
  3. $ \triangle LMN $ has angles in the ratio $1 : 1 : 1.$
  4. $ \triangle STW $ has sides in the ratio $1 : 1 : 1.$
  5. $ \triangle XYZ $ has sides in the ratio $4 : 3 : 2.$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Similar triangles must have the same ratio of angles. The ratio 2:3:4 is equivalent to 4:6:8 or any scalar multiple, but the order of the ratio matters for similarity. Option A provides the same ratio 4:3:2, which represents the same set of interior angles as 2:3:4.

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

The length of the sides of $\triangle DEF$ are $4,6,8$  $\triangle DEF \sim \triangle PQR$ for correspondence $DEF \leftrightarrow QPR$ if the perimeter of $\triangle PQR=36$, then the length of the smallest side of $\triangle PQR$ is_____

  1. $2$
  2. $4$
  3. $6$
  4. $8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sides of triangle DEF are 4, 6, and 8, giving a perimeter of 4 + 6 + 8 = 18. Triangle PQR is similar with a perimeter of 36, meaning the scale factor from DEF to PQR is 36/18 = 2. Multiplying the smallest side of DEF (which is 4) by this scale factor gives 4 * 2 = 8.