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#### Geometry Five Marks Questions

10th Standard EM

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. D and E are respectively the points on the sides AB and AC of a DABC such that AB=5.6 cm, AD=1.4 cm, AC=7.2 cm and AE = 1.8 cm, show that DE||BC

2.  DE||AC and DC||AP. Prove that $\cfrac { BE }{ CE } =\cfrac { BC }{ CP }$

3. Construct a triangle $\triangle$PQR such that QR = 5 cm, $\angle$P=30 and the altitude from P to QR is of length 4.2 cm.

4. Draw a triangle ABC of base BC = 8 cm, $\angle$A=60o and the bisector of $\angle$A meets BC at D such that BD = 6 cm.

5. In Fig, ABC is a triangle with $\angle$B=90o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.

6. Suppose AB, AC and BC have lengths 13, 14 and 15 respectively. If $\cfrac { AF }{ FB } =\cfrac { 2 }{ 5 } \quad \cfrac { CE }{ EA } =\cfrac { 5 }{ 8 }$. Find BD an DC

7. In a garden containing several trees, three particular trees P, Q, R are located in the following way, BP=2 m, CQ=3 m, RA=10 m, PC=6 m, QA=5 m, RB=2 m, where A, B, C are points such that P lies on BC, Q lies on AC and R lies on AB. Check whether the trees P, Q, R lie on a same straight line.

8. In $AD\bot BC$ prove that AB2+CD2 = BD2+AC2

9. BL and CM are medians of a triangle ABC right angled at A.
Prove that 4(BL+ CM2) = 5BC2.

10. Prove that in a right triangle, the square of 8. the hypotenure is equal to the sum of the squares of the others two sides.