Assignment (Basic Proportionality Theorem and its Converse)

1. In a triangle ABC, D and E are points on the sides AB and AC respectively such that DE BC.
i) If AD=4, AE=8, DB = x-4, and EC=3x-19, find x.
ii) If AD/BD = 4/5 and EC=2.5 cm, find AE.
iii) If AD=x, DB=x-2, AE=x+2 and EC=x-1, find the value of x.
iv) If AD=2.5 cm, BD=3.0 cm and AE=3.75 cm, find the length of AC.

2. In a triangle ABC, D and E are points on the sides AB and AC respectively. For each of the following show that DE BC.
i) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm
ii) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm

3. In a triangle ABC, P and Q are points on sides AB and AC respectively, such that PQ BC. If AP = 2.4 cm, AQ = 2.0 cm, QC = 3.0 cm and BC = 6.0 cm, Find AB and PQ.

4. In a triangle ABC, D and E are points on AB and AC respectively such that DE BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2.0 cm and BC = 5.0 cm, find BD and CE.

5. Using basic proportionality theorem, prove that any line parallel to the parallel sides of a trapezium divides the non parallel sides proportionally.

6. In the given figure, PA, QB and RC are each perpendicular to AC.
Prove that 1/x + 1/z = 1/y.

7. ABCD is a trapezium with AB CD. The diagonals AC and BD intersect each other at O. If AO = 2x+4, OC=2x-1, DO=3 and OB = 9x-21, Find x.

8. Prove that the line segments joining the mid points of adjacent sides of a quadrilateral form a parallelogram.

Activity related to Pythagoras Theorem

This project is contributed by Mayank X-B
Aim-To prove Pythagoras theorem by paper cutting and pasting.
Material Required-Thermocol,coloured sheets,cutter,scissors,sketchpens
ruler,fevistick .
Procedure-1 On a coloured sheet of paper draw triangle ABC with AB=3
units, BC=4 units and AC=5 units. Cut it out. (Taking 1 unit=1.5 inches)

2 Paste this triangle on a coloured sheet of paper covering a
thermocol

.
3 On AB paste a square ABDE of side=3 units

.
4 On BC paste a square BCFG of side=4 units.

5 On AC paste a square ACHI of side=5 units.


6 Make replicas of squares ABDE and BCFG.

7 Cut the replica of ABDE into 9 small squares each of area=1 sq unit.

8 Cut the replica of BCFG into 16 small squares each of area=1 sq unit.

9 Paste the unit squares obtained in step-7 and step-8 on square
ACHI.

Observation-The unit squares overlap square ACHI completely.

Result-Therefore, area of square ABDE + area of square BCFG = area of square
ACHI , ie ,
AB^2+ BC^2 = AC^2