Question

Use the given information to prove that 21 = 24. You are not allowed to use the Transitive Property for parallel lines.

DC || EG
DE || HF
∠CDE = ∠EFH
Prove: 21 = 24

A) 21 and 24 are alternate interior angles.
B) ∠CDE and ∠EFH are corresponding angles.
C) ∠CDE and ∠EFH are vertical angles.
D) ∠CDE and ∠EFH are supplementary angles.

Answer 1

Angle 21 is equal to angle 24 because they are corresponding angles created by a set of parallel lines, which makes them equal to each other by definition.

Step-by-step explanation:

The question asks us to prove that angle 21 is equal to angle 24 given a set of conditions about parallel lines and angles. To solve this problem, we need to use the information given about the parallel lines and corresponding angles to establish the relationships between the angles.

If lines DC and EG are parallel (DC || EG) and lines DE and HF are parallel (DE || HF), this establishes that angle CDE and angle EFH are corresponding angles (Option B). Corresponding angles are equal when the lines are parallel, so ∠CDE = ∠EFH.

Angles 21 and 24 are said to be ∠CDE and ∠EFH, respectively. Since we've established that these two are corresponding angles and thus equal, we can conclude that angle 21 is equal to angle 24.

The other options provided (alternate interior angles, vertical angles, supplementary angles) do not apply in this context because they describe different relationships between angles which are not supported by the information given in the question.