Question

which of the following statements is false?
a. vertical angles are always congruent.
b. when a pair of lines is cut by a transversal, the corresponding angles are always congruent.
c. inscribed angles that intercept the same arc are always congruent.
d. all right angles are congruent.
5.

Explanation:

• Option a: Vertical angles are formed by two intersecting lines and are always equal (congruent), so this is true.
• Option b: Corresponding angles are congruent only when the two lines cut by the transversal are parallel. If the lines are not parallel, corresponding angles are not congruent. So this statement is false.
• Option c: By the inscribed - angle theorem, inscribed angles that intercept the same arc are congruent. So this is true.
• Option d: All right angles measure $90^{\circ}$, so they are congruent. So this is true.

Answer:

b. When a pair of lines is cut by a transversal, the corresponding angles are always congruent.