Page 54 - Mathematics Class - X

ACTIVITY 4.2

OBJECTIVE
To verify the Basic Proportionality Theorem (Thales Theorem).

MATERIALS REQUIRED

Ruled paper Geometry box Sketch pens A pencil

PRE-REQUISITE KNOWLEDGE

1. Concept of parallel lines. 2. Concept of ratio and proportion.

THEORY
1. Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle to intersect the other
two sides in distinct points, the other two sides are divided in the same ratio.
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2. Area of a triangle, if its height is known, will be equal to × Base × Height.
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3. If two triangles are on the same base and between the same parallels, then their areas are also equal.

PROCEDURE:
1. Take a ruled sheet and draw three different triangles on it. You may choose an acute-angled triangle, an
obtuse-angled triangle and a right-angled triangle as shown in Fig. (a).
2. Name the triangles as ABC, PQR and XYZ respectively.

acute-angled triangle obtuse-angled triangle right-angled triangle
Fig. (a)

3. Mark any two parallel lines on each of them with sketch pens of different colours as shown in Fig. (b).
4. Name the lines as shown in the Fig. (b).

Fig. (b)
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