Final answer:
To prove that YS is perpendicular to XZ, we need to show that the angles formed between YS and XZ are right angles. Given that m angle 1 = m angle 2 and m angle 3 = m angle 4, we can use the transitive property of equality to show that m angle 1 = m angle 4. Therefore, YS is perpendicular to XZ.
Step-by-step explanation:
To prove that YS is perpendicular to XZ, we need to show that the angles formed between YS and XZ are right angles. Given that m angle 1 = m angle 2 and m angle 3 = m angle 4, we can use the transitive property of equality to show that m angle 1 = m angle 4. Since angles 1 and 4 are congruent and angle 1 is adjacent to angle 3, we can conclude that angle 3 is a right angle. Now, since YS is a transversal intersecting lines XZ and YZ, angle 3 is alternate interior to angle 2 and angle 2 is congruent to angle 4. Therefore, angle 2 is also a right angle, which means YS is perpendicular to XZ.