Tag: congruence

Questions Related to congruence

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

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

  1. False

  2. Both A and C

  3. True

  4. Not applicable

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Correct Option: C
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.

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?

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

  1. 23 m

  2. 32 m

  3. 42 m

  4. 24 m

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Correct Option: B
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.

There were three circular tracks made in a park having the same middle point but their radii was different. These tracks will be called

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

  1. Not similar

  2. Similar

  3. Congruent

  4. All of the above

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Correct Option: B
Explanation:

They are said to be similar as the shape is same but size differs.
Therefore, B  is the correct answer.

All ......... triangles are similar.

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

  1. Right angled

  2. Isoscles

  3. Equilateral

  4. Reflex

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Correct Option: C
Explanation:

All Equilateral  triangles , corresponding angles are equal .So, they are similar.
Therefore, C is the correct answer.

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