Similarity of Triangles

Q.

Question 6
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Q. In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

1. DE = BD
2. ∠ADE = ∠ACB
3. AE = AD
4. DE || BC

Q. In $△ABC,AB=3cm,AC=4cm$ and AD is the bisector of $\angle$A. Then, $BD:DC$ is

1. 0.25

Q.

$\text{In the figure given below, point D divides}\text{AB in the ratio 3 : 5 and DE is parallel to}\text{BC. If AE = 4.8 cm, then find the}\text{length of AC(in cm).}$

1. 12.8

Q. If in △ZXY and △FED, XY/EF = YZ/FD = XZ/ED, then which of the following option is true?

1. △XYZ ~ △DEF
2. △ZXY ~ △EDF
3. △XYZ ~△EFD
4. △ZXY ~ △EFD

Q.

In given figure $△$ ABC and $△$ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54$c{m}^2$ find the area of $△$ DEF .

Q. If two triangles are similar then their areas must be equal.

1. False
2. True

Q.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Apply the above theorem to the following :
The areas of two similar triangles $△ABCand△LMN\text{are}64c{m}^2\text{and}81c{m}^2$ respectively. If $MN=6.3cm$, find $BC.$

Q. In given figures sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ,QR$ and median $PM$ of $△PQR$. Show that $△ABC\sim △PQR$.

Q.

Find the measure of the sum of the angles of a pentagon.

Q. Two triangles are similar, if their corresponding angles are ________.

1. Proportional
2. Equal
3. A & B
4. None of the above

Q.

$\text{The corresponding sides of two triangles}△ABC\text{and}△PQR\text{are in the ratio 4:23.}$$\text{If}\angle B={60}^{\circ }\text{and}\angle A={40}^{\circ },\text{find the}\text{measure of}\angle R.$

1. ${80}^{\circ }$

2. ${90}^{\circ }$

3. ${100}^{\circ }$

4. ${110}^{\circ }$

Q. If two triangles are similar then their corresponding angles are equal.

1. True
2. False

Q.

$\Delta ABC\sim \Delta DEF$, with AB = 5 cm and DE = 8 cm.
If the area of $\Delta ABC$ is $50c{m}^2$, what will be the area of $\Delta DEF$ ?

1. $124c{m}^2$

2. $128c{m}^2$

3. $120c{m}^2$

4. $118c{m}^2$

Q. All ......... triangles are similar.

1. Right angled
2. Isoscles
3. Equilateral
4. Reflex

Q. Let $△ABC\sim △DEF$ and their areas be, respectively, $64c{m}^2$ and $121c{m}^2$. If $EF=15.4cm$, find $BC.$

Q.

Given, $\Delta ABC\sim \Delta PQR$.

Find the values of y and z.

1. $y=3\sqrt{3}$

2. $y=4\sqrt{3}$

3. $z=6$

4. $z=4$

Q.

The midpoint of the line joining the points (1, 2) and (5, 6) is

1. (3, 4)

2. (5, 1)

3. (4, 3)

4. (1, 3)

Q. Select the part of the sentence that has an error. If the sentence is correct select "No Error".

1. A
2. B
3. C
4. D
5. E

Q.

The areas of two similar triangles are $12c{m}^2$ and $48c{m}^2$. If the height of the smaller one is $2.1cm,$ then the corresponding height of the bigger one is

1. $4.41cm$

2. $8.4cm$

3. $4.2cm$

4. $0.525cm$

Q. If two triangles are similar, their corresponding angles are always _____.

1. right
2. obtuse
3. acute
4. equal

Q. In $\Delta ABC$, D and E lie on the line AB and AC respectively, as shown in the figure.
$\angle AED$ is:

1. 40

Q. $\text{If}\Delta ABC\sim \Delta MNP,AD\perp BC$
and $MQ\perp NP$ such that $\frac{AD}{MQ}=\frac{3}{6}$, then which of the following is correct?

1. area of $\Delta ABC=$ 2 area of $\Delta MNP$
   
2. area of $\Delta ABC=\frac{1}{4}$ area of $\Delta MNP$
   
3. area of $\Delta ABC=\frac{1}{2}$ area of $\Delta MNP$
   
4. area of $\Delta ABC=$ area of $\Delta MNP$

Q.

In the given figure, AX : XB = 3 : 5 and XY || BC.

Then, the ratio of the areas of trapezium XBCY and triangle ABC is

1. 64:55

2. 64:45

3. 45:64

4. 55:64

Q. Minimum number of pairs of equal corresponding angles to make two triangles similar = .

1. 2
2. 3
3. 1

Q.

If $\frac{AD}{BD}=\frac{3}{5}$, AC = 14 cm and $DE\parallel BC$ Find EC.

1. 8

2. 4.5

3. 8.75

4. 3

Q. For two triangles to be similar, the minimum pair of corresponding angles that should be equal is 3.

1. True
2. False

Q. If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR,$ respectively where $△ABC\sim △PQR$, prove that $\frac{AB}{PQ}=\frac{AD}{PM}$.

Q. Find out the error in the following sentences, if any. If there is no error, your answer is 'E'.
He reminded (A) me that he has often (B) told me not to play (C) with fire. (D) No Error.(E)

1. B
2. A
3. E
4. D
5. C

Q.

If $\frac{AD}{BD}=\frac{3}{5}$, AC = 14 cm and $DE\parallel BC$ Find EC.

1. 8

2. 4.5

3. 8.75

4. 3