Question

Question 1
Which statement describes the basis for the proof that vertical angles are congruent?
А
Two adjacent angles are always supplementary
B.
Two adjacent angles that form a linear pair are congruent.
с
Two angles that are each supplementary to a third angle are congruent.
D
Two angles that are each complementary to a third angle are congruent.

Answer 1

Answer:

C

Step-by-step explanation:

On each linear pair, there is one of the Vertical angles and an angle shared between the two angles. This means we can use the fact that supplements of the same angle are congruent.

Answer 2

The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

What are vertical angles?

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

In the provided figure.

∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)

∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)

According to transitive property, if a = b and b = c then a = c

Therefore,

∠1 + ∠2 = ∠1 + ∠4...(iii)

⇒∠2 = ∠4

Similarly, we can prove that

∠1 = ∠3

Therefore, we conclude that vertically opposite angles are always equal.

Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Thus, statement c is correct.

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