Jose uses the pattern in rows 1 and 8 in the multiplication table below to find ratios that are equivalent to 1:8. A multiplication table. In the row labeled 1, the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 are highlighted. In the row labeled 8, the numbers 8, 16, 24, 32, 40, 48, 56, 64, and 72 are highlighted.

If Jose extends the pattern in the highlighted rows to include a ratio that has a first term of 10, what would be the second term of the ratio?
10
20
80
90

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.