Similar Triangles

Q.

Question 7 (i)
In a right triangle ABC, B =90^o.

If AB= 6cm, BC= 8cm, find AC.

Q.

Can a triangle have two obtuse angles?

Q. Choose the correct option.

1. All similar triangles are congruent.
2. All congruent triangles are similar.
3. All congruent triangles cannot be similar.
4. Only some of the congruent triangles are similar.

Q.

The area bounded by the curve $y=x^2+4x+5$, the axes of co-ordinates and the minimum ordinate is

Q.

In triangles $\mathrm{ABC}$ and $\mathrm{DEF}$, $\angle \mathrm{B}=\angle \mathrm{E}$, $\angle \mathrm{F}=\angle \mathrm{C}$ and $\mathrm{AB}=3\mathrm{DE}$. Then, the two triangles are-

1. congruent but not similar

2. similar but not congruent

3. neither congruent nor similar

4. congruent as well as similar

Q. Standing at 5 cm apart from a vertical pole of height 3 cm, Sudha observed a building at the back of the piller that tip of the pillar is in line with the top of the building. If the distance between pillar and building is 10 cm, estimate the height of the building. [Here height of Sudha is neglected]

Q.

How many altitudes does an obtuse angled triangle have?

Q. 7 pillars are used to hold a slant rod as shown in the figure. If the distance between every two pillars is 1 m and first pillar is 1 m from the rod leg. Height of the last pillar is 10.5 m. Find the height of first pillar.

1. 1.5
2. 2.5
3. 3.5
4. 0.5

Q.

Which of the following are similar?

1. Circles

2. Squares

3. Equilateral triangles

4. All of the above

Q. In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test ?

Q. Which of the following statements is true for two similar triangles?

1. They are of the same shape.
2. None of the above is true.
3. Both a and b are true.
4. They are of the same size.
   

Q. Joe is fed up worrying about whether his neighbours can see into his living room from their house. He has decided to build a fence that is high enough to block the view from their top floor window. He needs to work out how high to build the fence. Find the minimum height of fence.

1. 2.675 cm
2. 2.744 m
3. 2.675 m
4. 2.75 cm

Q.

In a similar triangle,

I. The corresponding angles are equal.

II. The corresponding sides are always equal.

III. The corresponding sides are always proportional.

1. Only 1 is true.

2. Only 1 & 2 are true.

3. All are true.

4. Only 1 & 3 is true.

Q. Find the length of PQ (in m) from the given figure:

1. 25

Q.

In $△ABC$, the medians AD, BE and CF are drawn on sides BC, AC and AB respectively and $△ADC\sim △BEC$. What can you say about $△ABC$?

1. right angled

2. None of the above

3. isosceles

4. right angled isosceles

Q.

In the figure, ∆PQR ~ ∆XYZ, find 𝒂 and 𝒃.

Q. What are congruent triangles?

Q. Question 100

The actual length of a painting was 2 m. What is the length of the photograph if the scale used is 1 mm : 20 cm.

Q. Which of the following triangles is similar to the triangle shown below?

1. 
2. 
3. 
4. 

Q. Fill in the blanks using the correct word in the given bracket.
(iii) All ___ triangles are similar. (isosceles, equilateral).

Q. Question 101 (i)

Find the scale.
Actual size 12 m, Drawing size 3 cm

Q. In which of the following figures do the diagonals bisect each other at 90° and are equal in length?

1. Rectangle
2. Rhombus
3. Square
4. Circle

Q. State whether the given statement is true or false.
Congruent objects can be non-identical.

1. True
2. False

Q. If the sides of a triangle are in the ratio 2 : 4 : 5 and the perimeter of the triangle is 44 cm, the longest side of the triangle is .

1. 16 cm
2. 20 cm
3. 24 cm

Q.

BE and CF are two equal altitude of a triangle ABC. Using RHS congruency , prove that ∆ABC is isosceles.

Q.

$△PQR\cong △ABC$.If $\angle ABC=100°,$then $\angle PQR=$___________

Q. Standing 5 m apart from a vertical pole of height 3 m, Prabhas observed that the top of a building, situated at the back side of pole, is in line with the top of the pole. If the distance between pole and building is 20 m, estimate the height of the building.
[Here, height of Prabhas is neglected]

1. 9 m
2. 6 m
3. 10 m
4. 15 m

Q. Number of the corresponding parts of two congruent triangles is ___.

1. 3
2. 4
3. 6
4. 8

Q.

In ΔPQR ≅ ΔEFD,

(i) Which side of ΔPQR equals ED?

(ii) Which angle of ΔPQR equals angle E?

Q. If $\Delta ABC\sim \Delta PQC$, then choose the correct options (All lengths are in cm).

1. $\angle A=\angle P={45}^{\circ }$
2. $\angle A=\angle P={60}^{\circ }$
3. $PQ=1cm$
4. $PQ=2cm$