Introduction to Similar Triangles

Q.

If $A=\{x:x^2=1\}andB=\{x:x^4=1\}$ then $A△B$is equal to

Q.

$\text{If p and q are the roots of}\mathbf{}a{x}^2-bx+c=0,\mathbf{}a\ne 0\mathbf{}\mathbf{,}\mathbf{}\text{then find the value of}\mathbf{}p+q.$

Q.

When two triangles are similar, their corresponding sides are ___.

1. equal

2. proportional

3. in the ratio of 1:2:3

4. not proportional

Q.

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

1. True

2. False

Q. Statement I : If two triangles are similar, their sides are proportional.
Statement II: If two triangles are similar, their angles are equal.

1. Statement I is true but Statement II is false
2. Statement I is false but Statement II is true
3. Statement I and Statement II are true
4. Statement I and Statement II are false

Q.

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

1. True

2. False

Q.

Check whether the LHS and RHS are equal or not for the given value of $x$:

• 8x-3=4x+5 for x=2

Q.

If $\alpha$ and $\beta$are the roots of the quadratic equation$a{x}^2+bx+c=0$, observe the lists given below

List I	List II
A. $\alpha =\beta$	1.${\left(a{c}^2\right)}^{1/3}+{(a}^{}$
B. $\alpha =2\beta$	2. $2b^2=9ac$
C. $\alpha =3\beta$	3.$b^2=6ac$
D. $\alpha ={\beta }^2$	4.$3b^2=16ac$
	5.$b^2=4ac$
	6.${\left(a{c}^2\right)}^{1/3}+{\left(a^{2}c\right)}^{1/3}=b$

1. $A=5,B=2,C=4,D=6$

2. $A=5,B=2,C=1,D=4$

3. $A=5,B=4,C=2,D=6$

4. $A=5,B=2,C=4,D=1$

Q.

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

1. True

2. False

Q.

From the given triangles, which of the following is true?

1. $△ABC\sim △PQR$

2. $△ABC\sim △QPR$

3. $\angle ACB=\angle QRP$

4. $\angle BAC=\angle QPR$

Q. It is given that $△ABC\sim △PQR$ and $\angle B=\angle R={60}^{\circ }$. Find $\angle RPQ$.

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. ${90}^{\circ }$

Q. If $\Delta ABC\sim \Delta PQC,BC=16cm,AB=10cm,$ and $PQ=5cm$, then find the measure of $QR$.
[1 Mark]

A. $5cm$
B. $7cm$
C. $28cm$
D. $8cm$

Q.

If $y=x+\frac{1}{x}$, then

1. $x^2\left(\frac{dy}{dx}\right)+xy=0$

2. $x^2\left(\frac{dy}{dx}\right)+xy+2=0$

3. $x^2\left(\frac{dy}{dx}\right)-xy+2=0$

4. None of these.

Q. ABC is an isosceles triangle, right-angled at B. Similar triangles, $△ACD$ and $△ABE$ are constructed on sides AC and AB. Find the ratio of the areas of $\Delta ABE$ and $\Delta ACD$.

1. $1$
2. $\frac{2}{3}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q. If $\Delta ABC\sim \Delta TUS$, match value of $\frac{AB}{TU}=\frac{AC}{TS}=\frac{BC}{US}$ in each case.

1. 2.5
2. 0.67
3. 0.5

Q.

If triangle ABC is an isosceles triangle in which AB = AC = 13 cm, then find the value of $\frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}.$ (upto two decimal places)

1. 0.52

Q. $\Delta ABC\sim \Delta PQR,\text{If BC = 14 cm and}$
$\frac{AB}{PQ}=2,\text{then QR =}$ cm.

1. 3
2. 5
3. 7

Q. Which of the following is true?
Statement I : All similar triangles are congruent.
Statement II: All congruent triangles are similar.

1. Both statements are false
2. Both I and II
3. Only statement I
4. Only statement II

Q. $\text{If}\Delta ABC\sim \Delta PQR\text{and}$ $\Delta PQR\sim \Delta XYZ,\text{then}$ $\Delta ABC\sim \Delta XYZ$

1. True
2. False

Q.

Are the shown figures similar figures?

1. True

2. False

Q.

If triangle ABC is an isosceles triangle in which AB = AC = 13 cm, then find the value of $\frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}.$ (upto two decimal places)

1. 0.52

Q. What is the value of x in the figure if BD < DC?

1. 4

Q. In similar triangles,
1. The corresponding angles are equal.
2. The corresponding sides are always equal.
3. The corresponding sides are always proportional.

1. Only 1 is true.
2. Only 1 & 3 are true.
3. Only 1 & 2 are true.
4. Only 3 is true.

Q.

Are the below shown figures similar?

1. True

2. False

Q. Areas and ratio of angle bisectors of two similar triangles are given. Match the correct ratio in each case.

1. 9 : 7
2. 7 : 9
3. 1 : 2
4. 2 : 1

Q. What is the value of x in the figure if BD < DC?

1. 4

Q.

Are the shown regular hexagons similar figures?

1. True

2. False

Q.

S1: If two triangles are similar, sides are proportional.
S2: If two triangles are similar, angles are equal.

1. S1 is true but S2 is false

2. S1 is false but S2 is true

3. S1 and S2 are true

4. S1 and S2 are false

Q.

Find the root: $5=x+\frac{1}{2}$

Q.

If ∆𝐀𝐁𝐂 and ∆𝐏𝐐𝐑 are similar, then which of the following is true?

1. ∆ABC ≅∆PQR

2. None of these
3. $\frac{AB}{PQ}=\frac{BC}{QR}$

4. ∠ACB = ∠PQR