Dario purchased a 1-foot long piece of gum, and he decides to share it with 3 of his friends. So, he cuts the piece of gum into 4 equal pieces. However, another one of his friends also showed up, and there are now 5 people in total. Now that the gum will be shared equally among 5 people, will each person get more or less gum? Briefly state why you think so.

If he wishes to spilt it evenly there will be less for each person because they all have to give a peice to the other friend.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

inverse operation of addition