Difference between Congruency and Similarity

Q.

All congruent figures are similar but the similar figures need not be congruent.

1. True

2. False

Q.

Question 14
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the distance travelled by the balloon during the interval.

Q.

Question 14
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the distance travelled by the balloon during the interval.

Q.

A tower stands vertically on the ground. From a point on the ground, which is 24 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be ${60}^{\circ }$. Find the height of the tower.

1. $26\sqrt{3}m$

2. $24\sqrt{3}m$

3. $24m$
4. $26m$

Q.

A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from ${30}^{\circ }$ to ${60}^{\circ }$ as he walks towards the building. Find the distance he walked towards the building

1. 30

2. 20√3

3. 20

4. 30√3

Q. State the two properties which are necessary for given two triangles to be similar.

Q. In ∆ABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:

(i) ∆OMA ∼ ∆OLC
(ii) $\frac{\mathrm{OA}}{\mathrm{OC}}=\frac{\mathrm{OM}}{\mathrm{OL}}$

Q.

Sam is looking at the roof of the adjacent building from the top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of his line of sight of the tip of the other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building.

1. 10√3feet

2. 60 feet

3. 55feet

4. 55+10√3 feet

Q.

Question 6
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from ${30}^{\circ }to{60}^{\circ }$ as he walks towards the building. Find the distance he walked towards the building.

Q.

If three angles of a triangle are equal to the corresponding three angles of another triangle then the two triangles are congruent.

1. True
2. False

Q. In Figure 3, PQ || CD and PR || CB. Prove that $\frac{\mathrm{AQ}}{\mathrm{QD}}=\frac{\mathrm{AR}}{\mathrm{RB}}$.

Q.

In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that:

(i) ΔABC ∼ ΔAMP

(ii)

Q. If the ratio of the corresponding sides of two similar triangles is 1:1, then the triangles are congruent.

1. True
2. False

Q. Write True / False for the following statement:
Any two congruent figure are similar.

1. True
2. False

Q. State true or false:If a man standing on a platform 3 meters above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Q.

The length of a diagonal of square is√2(6+2√5)cm. Then find its length of side of square.

Q. Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A = 70⁰ PR = 9 cm, ∠P = 70⁰ and PQ = 4.5 cm. Show that
△ABC ∼ △PQR and state similarity theorem.

Q. If the ratio of the corresponding sides of two similar triangles is 1:1, then the triangles are congruent.

1. True
2. False

Q. Which of the following is a true statement?
(a) Two similar triangles are always congruent.
(b) Two figures are similar if they have the same shape and size.
(c) Two triangles are similar if their corresponding sides are proportional.
(d) Two polygons are similar if their corresponding sides are proportional.

Q.
The height of the building is feet long.

1. 55feet
2. 55+(50/$\sqrt{3}$)
3. 10$\sqrt{3}$ feet

Q.

The faces of a regular triangular pyramid are:

1. Congruent

2. Similar

3. Congruent but not similar

4. None of these

Q.

Consider two squares with 4 cm side each. Then which of the following is/are true?

1. The squares considered are similar.

2. The squares considered are congruent.

3. The squares considered are congruent, but not similar.

4. The squares considered are similar, but not congruent.

Q.

Sam is looking at the roof of the adjacent building from top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of his line of sight of the tip of the other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building?

1. 55feet

2. 10$\sqrt{3}$ feet

3. 55 + $\frac{50\sqrt{3}}{3}$ feet

4. 60cm

Q.
The height of the building is feet long.

1. 55+(50/$\sqrt{3}$)
2. 55feet
3. 10$\sqrt{3}$ feet

Q.

A point C on the level ground is at some distance from a 15 m pole AB. If the angle of elevation of the top of the pole from point C is 30°, then how far is point C from the foot of the pole?

1. ($15\sqrt{3}+1)m$

2. 15m

3. $15\sqrt{3}m$

4. 20m

Q. The faces of a regular triangular pyramid are:

1. Congruent and Similar
2. Neither congruent nor similar
3. Congruent but not similar
4. Similar but not congruent

Q. Which of the following statements are true/false ? Justify your answer.

1. Two squares are similar figures.
2. A triangle and a square are two figures which are not similar.
3. ​A polygon of 10 sides cannot be similar to a polygon of 12 sides.

Q.

The faces of a regular triangular pyramid are:

1. Congruent

2. Similar

3. Congruent but not similar

4. None of these

Q. In the given figure, there are two triangles. State whether the triangles are similar. Give reasons in support of your answer.

Q.
The height of the building is feet long.

1. 55feet
2. 55+(50/$\sqrt{3}$)
3. 10$\sqrt{3}$ feet