Similarity Rules of Triangles: Angle Angle Similarity Theorem

Q. If two angles of one triangle are equal to the corresponding two angles of another triangle then their sides are

1. Proportional
2. Equal
3. Parallel
4. Coincident

Q. Find the value of $x$ if the given triangles $△ABC\sim △PQR$.

1. ${40}^{\circ }$
2. ${80}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. In the given figure, find the length of $YZ$.

1. $37$ cm
2. $37.5$ cm
3. $38$ cm
4. $36$ cm

Q. The ladder is inclined to the top of the $12.3$ m high wall. Which of the following is length of the pole?

1. $4.1$ m
2. $3.01$ m
3. $12.3$ m
4. Cannot be determined

Q. For the figure given below, which of the following is/are correct?

1. $△ABC\sim △AED$
2. $\frac{AC}{AD}=\frac{AB}{AE}$
3. $\frac{AC}{AD}=\frac{BC}{ED}$
4. $\angle ABC=\angle AED.$

Q. In the given figure, $△ABC$ is a right angled triangle and $BD$ is perpendicular to $AC$. Which of the following is correct?

1. $△ABC\sim △ADB$
2. $△ADB\sim △BDC$
3. $△ABC\sim △BDC$
4. All of the above.

Q. A $40$ m high tower is $9$ m away from the point on the ground where there is a hook. A small pole is also standing in the exact middle of the tower and the hook. Now, a rope is tied to the top of the tower and to the hook on the ground, which is also touching the top of the pole.

The length of the middle pole and the rope tied to the tower and the hook are, respectively -

1. $20$ m and $41$ m
2. $25$ m and $45$ m
3. $30$ m and $44$ m
4. None