Question

What does the Vertical Angles Theorem state?

A. Two vertical angles are supplementary.
B. Two vertical angles are always obtuse.
C. Two vertical angles are congruent.
D. Two vertical angles are complementary.

In the proof, which postulate is used to show that the sum of angles m_1 and m_22 is equal to 180°?

A. Postulate 1
B. Postulate 2
C. Postulate 3
D. Postulate 4

What is the final conclusion of the proof?

A. Vertical angles are supplementary.
B. Vertical angles are congruent.
C. Vertical angles are complementary.
D. Vertical angles are obtuse.

Which property of equality is used in the proof to subtract m22 from both sides of the equation?

A. Property 1
B. Property 2
C. Property 3
D. Property 4

Answer 1

The Vertical Angles Theorem states that two vertical angles are congruent. In the proof, Postulate 3 is used to show that the sum of angles m_1 and m_2 is equal to 180°. The final conclusion of the proof is that vertical angles are congruent.

Step-by-step explanation:

The Vertical Angles Theorem states that two vertical angles are congruent. This means that if two lines intersect, the angles opposite each other (vertical angles) are equal in measure. So, option C is the correct answer for the first part of the question.

In the proof, to show that the sum of angles m₁ and m₂ is equal to 180°, Postulate 3 is used. Postulate 3 states that the sum of the interior angles of a triangle is 180°. Therefore, option C is the correct answer for the second part of the question.

The final conclusion of the proof is that vertical angles are congruent. So, option B is the correct answer for the third part of the question.

In the proof, the property of equality used to subtract m₂ from both sides of the equation is Property 3, which states that if a=b, then a-c=b-c. Therefore, option C is the correct answer for the fourth part of the question.