Tag: similarity of triangles

Questions Related to similarity of triangles

Anna went to the market to buy some boxes to store things. She was surprised to find boxes one inside the other. They were ....... boxes.

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

  1. Not similar

  2. Ambiguous

  3. Same size

  4. Similar

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Correct Option: D
Explanation:

As the boxes were fitting one inside the other they were similar as they were of same shape ,but their size was different.
Therefore, D is the correct answer.

If two triangles are ____ they are similar.

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

  1. Not equal

  2. Equiangular

  3. Different

  4. Not proportionate

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Correct Option: B
Explanation:

If the corresponding angles are equal then the triangles are similar .Hence if two triangles are Equiangular then the triangles are similar.

When one acute angle of a triangle is equal to one acute angle of other triangle, and the triangles are right angles, do you think the triangles are similar?

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

  1. Not sure

  2. Similar

  3. Not similar

  4. Cannot be possible

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Correct Option: B
Explanation:

Given one acute angle is equal and both triangles are right angled . Hence one angle of both triangles is $90^{\circ}$ each.

Hence the triangles are similar by $AA$ similarity criteria.
Option $B$ is correct.

If corresponding angles of two triangles are equal, then they are known as

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

  1. Equiangular triangles

  2. Adjacent angles

  3. Supplementary angles

  4. Complementary angles

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Correct Option: A
Explanation:

If corresponding angles of two triangles are equal, then they are known as Equiangular triangles.

Option $A$ is correct.

If the angles of one triangle $ABC$ are congruent with the corresponding angles of triangle $DEF$, which of the following is/are true?

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

  1. The two triangles are congruent but not necessarily similar.

  2. The two triangles are similar but not necessarily congruent.

  3. The two triangles are both similar and congruent.

  4. The two triangles are neither similar nor congruent.

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Correct Option: B
Explanation:

Only the angles of two triangles being congruent meaning the same, implies that the triangles are similar, since there could be many triangles having those angles but of varied sizes, just enlarging the sides in proportion.

For congruency, atleast one side has to be taken into account while writing the congruency test.

Which of the following is true?

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

  1. The ratio of sides of two similar triangles is same as the ratio of their corresponding altitudes.

  2. The ratio of sides of two similar triangles is same as the ratio of their corresponding perimeters.

  3. The ratio of sides of two similar triangles is same as the ratio of their corresponding area

  4. The ratio of sides of two similar triangles is same as the ratio of their corresponding medians.

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Correct Option: A
Explanation:

Option A is correct as it is the property of similar triangle

If the area of two similar triangles are equal, then they are

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

  1. equilateral

  2. isosceles

  3. congruent

  4. not congruent

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Correct Option: C
Explanation:

They are congruent.

$Consider\triangle ABC\quad and\triangle PQR$
$ \cfrac { ar(\triangle ABC) }{ ar(\triangle PQR) } =\cfrac { { AB }^{ 2 } }{ { PQ }^{ 2 } } =\cfrac { { AC }^{ 2 } }{ { PR }^{ 2 } } =\cfrac { { BC }^{ 2 } }{ { QR }^{ 2 } } $
$\implies\quad AB=PQ,\quad AC=PR,\quad BC=QR$
$ \therefore The\triangle ABC\quad$ and $\triangle PQR$  are congruent.

Two polygons of the same number of sides are similar if all the corresponding interior angles are:

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

  1. Equal

  2. Proportional 

  3. Congruent

  4. Cannot say

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Correct Option: D
Explanation:

Two polygons of the same number of sides are similar, if: 

(a) Their corresponding angles are equal. 
(b) Their corresponding sides are in the same ratio (Proportional).
Hence, nothing can be said about two given polygons when only the angles are congruent, is known.

Triangle is equilateral with side$A$, perimeter $P$, area $K$ and circumradius $R$ (radius of the circumscribed circle). Triangle is equilateral with side $a$, perimeter $p$, area $k$, and circumradius $r$. If $A$ is different from $a$, then

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

  1. $P : p = R : r$ only sometimes

  2. $P : p = R : r$ always

  3. $P : p = K : k$ only sometimes

  4. $R : r = K : k$ always

  5. $R : r = K : k$ only sometimes

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Correct Option: B
Explanation:

Since the triangles are similar, we have $A:a = P:p = R:r = \sqrt {K}: \sqrt {k}$ always, so that (b) is the correct choice.

If in two triangles, corresponding angles are _______ and their corresponding sides are in the ______ratio and hence the two triangles are similar.

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

  1. equal, same

  2. unequal, same

  3. equal, different

  4. unequal, different

Show answer
Correct Option: A
Explanation:

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