Question

Proving that Vertical Angles Are Congruent
Examine the following diagram:

2 lines intersect to form 4 angles. From the top, clockwise, the angles are 1, 4, 2, 3.

Which statement is not true of the given diagram?
m∠2 + m∠3 = 180°
m∠2 + m∠4 = 180°
∠3 and ∠4 are vertical angles
∠2 ≅ ∠4

Answer 1

The false statement is: ∠2 ≅ ∠4.

Reason: Angles 2 and 4 are adjacent (they form a linear pair), so m∠2 + m∠4 = 180° (they are supplementary), not necessarily equal. The other statements are true: ∠2 + ∠3 = 180° and ∠2 + ∠4 = 180° because each is a linear pair with ∠2, and ∠3 and ∠4 are vertical (opposite) angles, so they are congruent.