Question

1) Constructions revisited: a. Perform a bisection of angle with only a compass and straight edge. Leave construction lines as as a part of showing your work. b. Inscribe the regular polygon of your choice in a circle (triangle, square, pentagon, hexagon, etc.). Provide step- by-step instructions as if you were teaching a young geometry student the process.

Answer 1

solution FM Process: (Contruction). suppose we have to besect a gives. angle LAOB (say 60°). put the point of compass on point o. • Make an arc, by keeping compass on point o through CFE. IF & E are intersection pents on o B and oa respectively). Now, put the noodle of compass on E and construct as arc HG' and again make an. are I ] by putting the compass ont Join the meeting point of arc (II and HG) le K to point Thus, dire 'Ok' is the bisector of angle AOB. e il LAOB=60 LKOA=LKOB=30° (6) Conspuction • Suppose, we have to draw an inscribed square. • Draw a crcle of any radius (say, OA). • Draw a diameter through centre'o', cutting circumference of cicle at A&B.

Bisect perpendicularty, the dia meler, AB put the compass needle on A and stretch it slightly greater than 'Oh and make an arc above and below of drameter AB. o put the same stretched compass on B' and make are, above and below. of diameter AB, thus cutting the are of bath positions (say, C, D) • Join , CD and extend it such that it intersects the wide at E and F. Join all points a tof, F to B, B to E, Eto A. Thus ABEF AFBE is our required square inscribed in a wille Check ( diagonals EF LAB. e diagonals EF and AB bisect each other meso Each diagonals are equal ( because both are diameters) all are properties of a square