ab=4cm,∆B=70°,∆C=30°,scale factor 7/5
Answers
Maths
Construct a △ABC in which AB=4 cm, BC=5 cm and AC=6 cm. Now, construct a triangle similar to △ABC such that each of its sides is two-third of the corresponding sides of △ABC. Also, prove your assertion.
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,
ABAB′=AA3AA2=32
also B′C′∥BC
∴∠AB′C′=∠ABC
In △AB′C′,△ABC
∠A=∠A
∠AB′C′=∠ABC
△AB′C′∼△ABC
⇒ABAB
