Number 2:
m∠1 + m∠2 = 180 and definition of supplementary angles.
Remember that a supplementary angle is two angles that add up to be 180. Thus, makes the proof correct.
Number 3:
∠1 ≅ ∠2, ∠3 ≅ ∠4 and given.
This is correct because this proof is given in the question.
Number 4:
m∠1 = m∠2, m∠2 = m∠1 and definition of congruence.
A congruent angle means that they both have the same angle measure. As you can tell by the image, they give you a rectangle and all the angles are right (90°) which means they are congruent. Thus, proves this proof.
Number 5:
2m∠2 = 90 and transitive property of equality.
Transitive property of equality means if x = y then y = z then z = y. Since all the angles in a rectangle are the same (90°), makes the proof true.
Number 6:
m∠2 = 90 and division prop of equality.
Division prop of equality means that if you divide a non-zero number to both sides, it remains the same. Going back to the last one, all the angles are 90°, thus they remain the same.
Number 7:
m∠3 = 90 and substitution property.
Substitution property means that x = y and that x can be substituted for y and y can be substituted for x. Again, all the angles are the same so x could equal 90 for y and y could equal 90 for x.
Number 8:
∠3 is a right angle and definition of right angles.
A right angle is an angle that measure 90°. Thus proves the proof.
Best of Luck!
