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#### Geometry Two Marks Question

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. Is $\triangle$ABC~$\triangle$PQR?

2. A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.

3. $\angle A=\angle CED$ prove that $\Delta\ CAB \sim \Delta CED$ Also find the value of x.

4. If $\triangle$ABC is similar to$\triangle$DEFsuch that BC=3 cm, EF=4 cm and area of $\triangle$ABC= 54 cm2. Find the area of $\triangle$DEF.

5. An insect 8 m away initially from the foot of a lamp post which is 6 m tall, crawls towards it moving through a distance. If its distance from the top of the lamp post is equal to the distance it has moved, how far is the insect away from the foot of the lamp post?

6. P and Q are the mid-points of the sides CA and CB respectively of a $\triangle$ABC, right angled at C.4(AQ2+BP2)=5AB2

7. An Aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1½ hours?

8. In figure if PQ || RS Prove that $\Delta POQ\sim \Delta SOQ$

9. In figure OA· OB = OC·OD
Show that $\angle A=\angle C\quad and\quad \angle B=\angle D$

10. In figure the line segment xy is parallel to side AC of $\Delta ABC$ and it divides the triangle int two parts of equal areas. Find the ratio $\cfrac { AX }{ AB }$