Question

Construct a triangle ABC in which AB - 4 cm, AC 5.2 cm and ZA 135". Also bisect
Construct
A and B
90", ZA 45" and BC 5 cm.
= 4 , = ".​

Answer 1

Answer:

Answer

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

=

3

2

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