Question

Use a paragraph proof to prove the converse of the corresponding angles postulate.

Answer 1

What is the converse? I am not too good with proofs.

Answer 2

Converse: (1) If an object is a polygon then it is a triangle (false). A square is a polygon but not a triangle. (2) If a number is divisible by two then it is even (true). Of course the first one is false because not all polygons are triangles.

Answer 3

If the angles are congruent angles they are corresponding angles.

Answer 4

I'm not sure if this is the correct way to do it but here goes:

Angle 1 + angle 4 = 180 degrees and angle 4 + angle 5 = 180 degrees. Therefore angle 1 + angle 4 = angle 4 + angle 5. Based off of this statement, angle 1 = angle 5. Since these are the same value, the line segments are parallel. The law of corresponding angles states that if two lines are intersected by another line and the angles formed by those 2 lines and the line intersecting them are the same, the lines are parallel.

Answer 5

2 = 6 given
2 + 3 = 180 (straight angle)
2 + 6 = 180
sum of co-interior is 180 => AB||BC

Answer 6

You have to use justifications to "prove" something in geometry or algebra...

Answer 7

It is given that Corresponding angles are congruent. To prove that ∠2=∠6, first use the Definition of Supplementary Angles to confirm that ∠2+∠1=180 and ∠6+∠5=180. Then, use the Substitution Property of Equality to show that ∠2+∠5=180. Finally, use the Transitive Property of Equality to prove that ∠2+∠5=∠5+∠6 and therefor ∠2=∠6 according to the Subtraction Property of Equality.

Answer 8

Lines r and s are parallel as given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.