Tag: introduction to shapes

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Questions Related to introduction to shapes

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

  1. Not similar

  2. Ambiguous

  3. Same size

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

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

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?

  1. Not sure

  2. Similar

  3. Not similar

  4. Cannot be possible
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

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

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

Which of the following is true?

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

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

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

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

  1. equilateral

  2. isosceles

  3. congruent

  4. not congruent
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. Equal

  2. Proportional

  3. Congruent

  4. Cannot say
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

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

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

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

  1. equal, same

  2. unequal, same

  3. equal, different

  4. unequal, different
Reveal answer Fill a bubble to check yourself
A Correct answer
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.