Question

Draw an ∠BAC of measure 50° such that AB = 5 cm and AC = 7 cm. Through C draw a line parallel to AB and through B draw a line parallel to AC, intersecting each other at D. Measure BD and CD.

Answer 1

Steps of construction:

1. Draw angle BAC = 50$°$ such that AB = 5 cm and AC = 7 cm.
2. Cut an arc through C at an angle of 50$°$.
3. Draw a straight line passing through C and the arc. This line will be parallel to AB since $\angle CAB=\angle RCA=50°$.
4. Alternate angles are equal; therefore the line is parallel to AB.
5. Again through B, cut an arc at an angle of 50$°$ and draw a line passing through B and this arc and say this intersects the line drawn parallel to AB at D.
6. $\angle SBA\hspace{0.17em}=\angle BAC=50°$, since they are alternate angles. Therefore BD$\parallel$AC.
7. Also we can measure BD = 7 cm and CD = 5 cm.