Page 49 - Mathematics Class - X

Unit 4 Geometryy
Geometr

ACTIVITY 4.1

OBJECTIVE
To establish the criteria for similarity of two triangles.

MATERIALS REQUIRED

Cardboard Glue
Chart Paper Pen/Pencil
Graph Paper Ruler

PRE-REQUISITE KNOWLEDGE
1. Knowledge of Basic Proportionality Theorem (BPT)
2. Concept of similarity of figures

3. Concept of similarity of triangles

THEORY

1. Basic Proportionality Theorem (BPT): If a line is drawn parallel to one side of a triangle to intersect the
other two sides in distinct points, then the other two sides are divided in the same ratio.

This theorem is also called Thales theorem. In ∆ABC, DE is parallel to BC, intersecting AB at D and AC
at E. Then, according to Basic Proportionality theorem, A

AD = AE
DB EC
D E

B C

2. Converse of the theorem is also true, i.e. if a line divides any two sides of triangles in the same ratio, then
the line must be parallel to the third side.

PROCEDURE

Case 1

1. Cut out two triangles ABC and PQR with their corresponding angles
equal using a coloured paper.

2. In the ∆ABC and ∆PQR, ∠A = ∠P; ∠B = ∠Q and ∠C = ∠R.

Fig. (a)
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