Question

(a) Construct a AABC in which AB 4 cm, BC 6 cm
and AC 7 cm. Construct its similar ABC
whose side AB = 5 cm
GE​

Answer 1

Step-by-step explanation:

Steps:

1. draw base AB=4cm

2. with A as center, with a scale of 5cm as radius draw an arc and with B as center, with a scale of 6cm as radius draw an arc.

3. let C be the point of intersection of the above 2 lines.

4. draw a ray AX making an acute angle with line AB on the opposite side if the vertex C.

5. mark 3 points A1,A2,A3 such tha A1A2=A2A3=A3A1

6. join A3B and draw a parallel line B

′

A2

7. draw a line parallel to BC to intersect AC at C

′

Thus AB

′

C

′

is a required triangle.

Justification;

By construction,

AB ' / AB= AA3/AA2 = 32

also B ′ C ′ ∥ BC

∴∠AB ′ C ′ =∠ABC

In △AB ′ C ′ ,△ABC

∠A=∠A,∠AB ′ C ′=∠ABC

△AB

′

C

′

∼△ABC

⇒

AB

AB

′

=

AC

AC

′

=

BC

B

′

C

′

∴

AB

AB

′

=

AC

AC

′

=

BC

B

′

C

′

=

3

2

solution