If side AC measures 5cm and BC measures 4cm What will be the measure of AB?
Answers
If side AC measures 5cm and BC measures 4cm What will be the measure of AB?If side AC measures 5cm and BC measures 4cm What will be the measure
Answer:
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