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Online Quiz (Worksheet A B C D)

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High School Mathematics - 2
8.1 Basic Proportionality Theorem or Thale's Theorem

A straight line drawn parallel to a side of a triangle, divides the other two sides proportionally.
Data: Triangle ABC, D is a point on AB and the line DE is parallel to BC
To prove: AD/BD = BE/CE

Consider triangle ABC and triangle BDE
StepStatement Reason
1ang BAC = ang BDECorresponding angles because DE ll AC
2ang BCA = ang BEDCorresponding angles because DE ll AC
3ang DBE = ang ABCCommon angle
4triangle ABC lll triangle BDEAAA postulate on similarity
5AB/BD = BC/BEcorresponding sides are proportional
6(BD+DA)/BD =(BE+EC)/BESplit AB and AC
71+AD/BD = 1+CE/BESimplification
8AD/BD = CE/BESubtract 1 from either sides
10AD/BD= BE/CEReciprocating

We shall try to prove the converse of basic proportionality theorem.
Let us consider triangle ABC shown in the figure below.

Divide the sides of the triangle AB and AC into any number of equal parts.
By measuring the angles B1 and B we observe that they are equal.
But B1 and B are corresponding angles.
Hence B1C1 ll BC.
AB2/B2 B= AC2/C2C = 2/3 and B22C2 ll BC
AB3/B3B =AC3/C3C= 3/2 and B3C3 ll BC
AB4/B4B = AC4/C4C and B4C4 ll BC

Example: In the figure, find the length of PS given that ST ll QR.

Let PS = x cm
As ST ll QR
x/3 = 3/2
x = 9/2
Answer: PS = 4.5 cms

Directions: Answer the following questions.
Q 1: A research team wishes to determine the altitude of a mountain as follows: They use a light source at L, mounted on a structure of height 2 meters, to shine a beam of light through the top of a pole P' through the top of the mountain M'. The height of the pole is 20 meters. The distance between the altitude of the mountain and the pole is 1000 meters. The distance between the pole and the laser is 10 meters. We assume that the light source mount, the pole and the altitude of the mountain are in the same plane. Find the altitude h of the mountain.
500 metres
1000 metres
1820 metres

Q 2: In a trapezium ABCD, AB ll CD. Its diagonals AC and BD intresect at O. Then AO.OD = BO.OC

Q 3: ABC is a triangle in which D and E are the points on AC and BC. DE ll AB. CD = 15 cms, AB = 11 cms, DE = 7cms. Find the length of CD

Q 4: The diagonals AC and BD of a quadrilateral ABCD intersect at O such that AO/OC = BO/OD. In such a case, ABCD becomes a trapezium.

Q 5: M and N are points on the sides PQ and QR of triangle PQR. If PM is 4, QM = 4.5, NR = 4.5 cm. find the length of PN
4.5 cm
4 cm

Q 6: In the figure, is PQ ll EF. State yes or no.


Q 7: In triangle ABC, D and E are the points on AB and AC. BD = 30, DA = x, BF = y, EC = 15, AC = 22. Find AD.

Q 8: ABC is a triangle. D and E are points on AB and AC. If BD = 4 cms, AD = 8 cms, CE = 9 cms. Find BE.
2.5 cms
3.5 cms
4.5 cms

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Question 10: This question is available to subscribers only!

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