Error analysis. find and correct all 3 of the errors in the proof.( 3 points)

The correct reason for is property of corresponding angles and the reason for is substitute and the third error is the forget the property that the sum of consecutive interior angles is 180.

Explanation:

It is given that m is parallel to n.

When  two parallel lines intersected by a transversal eight angles are produced as shown in the given figure, where m and n are parallel and l is the transversal line.

In this case corresponding angles are congruent. Example , etc.

So, by the property of corresponding angles.

because these are supplementary angles.

Substitute

So, the correct reason is substitution.

Hence proved

The third error is the forget the property that the sum of one side interior angles is 180. Since the alternate interior angles are congruent therefore the consecutive interior angles are supplementary angles around the sum of consecutive interior angles is 180 degree.

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.