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

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

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

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

All congruent figures are similar but the similar figures are not congruent.Is this statement true or false?

  1. False

  2. Both A and C

  3. True

  4. Not applicable
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Congruent figures are of same shape and size. So they are similar but similar figures are not congruent as they might not be of the same size.
Therefore, C is the correct answer.

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

A tree of height 24m standing in the middle of the road casts a shadow  ofheight 16m. If at the same time a nearby pole of 48 m casts a shadow , what would the height of the shadow be?

  1. 23 m

  2. 32 m

  3. 42 m

  4. 24 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the ratio of the tree is 3 : 2 = 24 m : 16 m 
The ratio of the pole is  same so 48m : 32m
Therefore, B is the correct answer.