Similar Figures

Q. What is the meaning of area of cross section??

Q. If $\Delta PMN\sim \Delta ADB$, then which of the following is always true?

1. PM = AD
2. $\frac{PN}{AB}=\frac{MN}{AD}$
   
3. $\angle PNM=\angle ADB$
4. $\frac{PM}{MN}=\frac{AD}{BD}$
   

Q.

If $X=5Y$, then $X$ and $Y$ vary ______ with each other.

Q.

State whether the following quadrilaterals are similar or not:

Q.

In figure, express x in terms of a, b and c.

Q.

An equilateral triangle can be a right triangle.

1. True
2. False

Q. Question 2
For which of the following, diagonals bisect each other?
a) Square
b) Kite
c) Trapezium
d) Quadrilateral

Q.

ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If $AB=3.6cm,AC=2.4cm$ and $AD=2.1cm,$ then AE is equal to

1. 1.05 cm

2. 1.4 cm

3. 1.2 cm

4. 1.8 cm

Q. Question 119
State whether the statements are True or False.
Every square is a parallelogram.

Q. Question 2 (ii)
Give two different examples of pair of

(ii) Non-similar figures

Q.

Which statements are true about dilations? Select all that apply.

1. Dilations produce images that are similar to the pre-image.

2. Dilations produce images that are always congruent to the pre-image.

3. Dilations produce images that have angles that are congruent to the pre-image.

4. Dilations produce images that have sides that are congruent to the pre-image.

5. Dilations produce images that have sides that are proportional to the pre-image

Q.

Fill in the blanks using the correct word given in brackets:
(i) All circles are ___ (conruent, similar).
(ii) All squares are ___ (similar, congruent)
(iii) All ___ triangles are similar (isoscles, equilaterals):
(iv) Two triangles are similar, if their corresponding sides are ___(propotional, equal)
(v) Two traingles are similar, if their corresponding sides are ___(proportional equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding are ___ (equal, proportional)

Q. The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm² is

(a) Rs. 1582.50

(b) Rs. 1724.50

(c) Rs. 1683

(d) Rs. 1642

Q.

In an Isosceles triangle, two angles are always _________.

Q.

Water in a canal $1.5\mathrm{m}$ wide and $6\mathrm{m}$ deep is flowing with a speed of $10\mathrm{km}/\mathrm{hr}$. How much area will it irrigate in $30\mathrm{minutes}$ if $8\mathrm{cm}$ of standing water is desired?

Q.

Which of the following statements is false?

1. All isosceles triangles are similar.

2. All equilateral triangles are similar.

3. All circles are similar.

4. None of the above.

Q. A line drawn parallel to one side of a triangle divides the other two sides in ___ .

1. the ratio 1:3
2. the ratio 1:2
3. the same ratio
4. different ratios

Q. A model of a ship is made to a scale 1 : 300 [3 MARKS]
i) The length of the ship is 2m. Calculate the length of the ship.
ii) The area of the deck ship is 180, 000 $m^2$. Calculate the area of the deck of the model.
iii) The volume of the model is $6.5m^3$. Calculate the volume of the ship.

Q. In the given figure, DE and BF are the bisectors of ∠ADC and ∠CBA respectively. If DE = BF, AD || BC, AD = BC, AE = 4 cm and BE = 6 cm, then FC + DF equals

दिए गए चित्र में, DE तथा BF क्रमशः ∠ADC तथा ∠CBA के समद्विभाजक हैं। यदि DE = BF, AD || BC, AD = BC, AE = 4 cm तथा BE = 6 cm है, तब FC + DF बराबर है

1. 12 cm
2. 8 cm
3. 9 cm
4. 10 cm

Q.

State whether the following quadrilaterals are similar or not:

Q.

The dimensions of the model of a multistorey building are $1.2m\times 75cm\times 2m$. If the scale factor is 1:30; then the actual dimensions of the building are

1. $32m\times 24.5m\times 54m$

2. $26m\times 12.5m\times 50m$

3. $36m\times 22.5m\times 60m$

4. $26m\times 22m\times 40m$

Q. The cost of painting the four walls of a room 12 m long at ₹30 per m² is ₹7560 and the cost of covering the floor with mat at ₹25 per m² is ₹2700. Find the dimensions of the room.

Q.

Find the least number of square tiles required to pave the ceiling of a room $15m17cm$, long and $9m2cm$ broad.

Q. Question 6
Which of the following figures satisfy the following properties?
-All sides are congruent.
-All angles are right angles.
-Opposite sides are parallel.

Q. The dimensions of a room are 14 m × 10 m × 6.5 m. There are two doors and 4 windows in the room. Each door measures 2.5 m × 1.2 m and each window measures 1.5 × 1 m. Find the cost of painting the four walls of the room at Rs 35 per m².

Q.

An oval-shaped meeting table made of wood has dimensions of its top as $10m$ and $6m$. Find the cost of polishing it at $Rs.5.75$ per $sq.m.$

Q. Question 2
It is given that $\Delta DEF\sim \Delta RPQ$. Is it true to say that $\angle D=\angle Rand\angle F=\angle P?$ why?

Q. Question 8
If in two right triangles, one of the acute angles of one triangle is equal to an acute of the other triangle. Can you say that two triangles will be similar? Why?

Q.

A tent is of the shape shown in the given figure. The area of the floor under the tent is 64π m². (Use = π = ²²/₇)

If 1 square metre of canvas costs Rs 5, then what is the cost of the canvas required for making the tent?

1. Rs 3771

2. Rs 8553

3. Rs 7542

4. Rs 4274

Q.

A model of a ship is made to a scale 1 : 300.
(i) The length of the model of the ship is 2 m. Calculate the length of the ship.
(ii) The area of the deck of the ship is 180, 000 $m^2$. Calculate the area of the deck of the model.
(iii) The volume of the model is 6.5 $m^3$. Calculate the volume of the ship.