AAA Similarity

Q.

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

1. ${90}^{\circ }$

2. ${120}^{\circ }$

3. ${60}^{\circ }$

4. ${30}^{\circ }$

Q. The triangles $\Delta ABC$ and $\Delta PQC$ are similar by which similarity criteria?

1. SSS
2. SAS
3. AA
4. ASA

Q. Statement I: Two triangles are similar if two corresponding angles are equal.
Statement II: The sum of internal angles in a triangle is ${180}^{\circ }$.

1. Statement I is true. Statement II is true. Statement II is the correct explanation of Statement I.
2. Statement I is true. Statement II is false.
3. Statement I is true. Statement II is true. Statement II is not the correct explanation of Statement1.
4. Statement I is false. Statement II is true.

Q. In the given figure, $x$ is

1. $\frac{ac}{b+c}$
2. $\frac{ac}{a+c}$
3. $\frac{ab}{a+b}$
4. $\frac{bc}{b+c}$

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

1. True
2. False

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. Both (i) and (ii) are true

2. Only (i) is true

3. Only (ii) is true

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

Q.

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

1. $△ABC\sim △PQR$

2. $△ABC\sim △QPR$

3. $△BAC\sim △QRP$

4. $△BAC\sim △QPR$

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. 4 cm

2. 8 cm

3. 2 cm

4. 6 cm

Q.

Refer to the figure: DE is parallel to BC.

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

1. 

2. 

3. 

4. 

Q.

In $△ABC$ , D, E and F are mid points of sides AB , BC and AC respectively.How many pairs of similar triangles are there in the figure formed after joining D, E, F ?

1. 4

2. 6

3. 8

4. 10