AAA similarity

Q.

$△$ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?

i) $△ABC\sim △$ ADE

ii) $\frac{AD}{BD}=\frac{AE}{EC}$

iii) $DE=\frac{BC}{2}$

1. (i), (ii) and (iii)

2. (ii) and (iii) only

3. (i) and (ii) only

4. Only (i)

Q.

If $△ABC\sim △PQR$ and $\angle B=\angle R={60}^{\circ }$, then find $\angle$ RPQ.

1. ${60}^{\circ }$

2. ${30}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q.

The triangles ABC and ADE are similar.

Which of the following is true ?

1. $\frac{AB}{AD}=\frac{BC}{DE}$
2. $\frac{BC}{BD}=\frac{CE}{DE}$

3. $\frac{EC}{AC}=\frac{AD}{DE}$

4. All of the above.

Q.

In an equilateral triangle PQR, if p, q and r denote the lengths perpendiculars from P, Q, R respectively on the opposite sides, then –

1. p ≠ q = r

2. p = q ≠ r

3. p ≠ q ≠ r

4. p = q = r

Q.

Refer to the figure: DE is parallel to BC.

$\frac{AD}{DB}$ = ?

1. 

2. 

3. 

4. 

Q.

Refer to the figure shown:

In the given diagram, ABCD is a rectangle. BC is extended to E such that C is the midpoint of BE. The points A and E are joint to meet DC in P. Then

i) P is the midpoint of AE.

ii) P is the midpoint of CD.

1. Only (ii) is true

2. Neither (i) nor (ii) is true

3. Both (i) and (ii) are true

4. Only (i) is true

Q.

In the given triangle DE II BC, which of the following statements is true?

1. $\frac{AD}{AB}=\frac{DE}{BC}$

2. $\frac{AB}{AB}=\frac{DE}{BC}$

3. $\frac{AD}{AB}=\frac{DB}{BC}$

4. $\frac{AB}{AB}=\frac{DC}{BC}$

Q. In the given figures which of the triangles are similar?

1. $\Delta DEF\sim \Delta SQR$
2. $\Delta FED\sim \Delta PQS$
3. $\Delta PQS\sim \Delta QRS$
4. $\Delta EDF\sim \Delta QPS$

Q. We only need to check if the corresponding angles are equal for two triangles to be similar.

1. True
2. False

Q.

In the adjoining figure, AB = 10 cm, BC =15 cm AD : DC = 2 : 3, then $\angle$ABC is equal to -

1. ${30}^{\circ }$

2. ${40}^{\circ }$

3. ${45}^{\circ }$

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

Q.

$\text{XY is drawn parallel to the base BC of a}\Delta ABC\text{cutting AB at X and AC at Y. If}\text{AB = 4 cm, BX and YC = 2 cm,}$
$\text{then find the measure of AY .}$

1. 2 cm

2. 4 cm

3. 6 cm

4. 8 cm