Danny draws a transversal, t, on two parallel lines AB and CD, as shown below:

Two parallel lines are shown cut by a transversal labeled t. 1, 2, 7 and 8 are marked clockwise as exterior angles. 4, 3, 6, an

He makes the following table to prove that the alternate interior angles are equal:

Statement Justification
angle 2 = angle 6 ?
angle 2 = angle 4 Vertical angles are congruent.
angle 4 = angle 6 transitive property of equality,
angle 2 = angle 6,
angle 2 = angle 4,
therefore angle 4 = angle 6
Which is the missing justification?

The missing justification is Corresponding angles are congruent. Here's why: Step-by-Step Explanation 1. Understanding the Problem: We need to find the reason why angle 2 is equal to angle 6. Danny has already established that angle 2 is equal to angle 4 (vertical angles) and angle 4 is equal to angle 6 (transitive property). Therefore, we need to find the relationship between angle 2 and angle 6 directly.2. Identifying the Relationship: Angle 2 and angle 6 are in corresponding positions relative to the transversal and the parallel lines. They both appear in the same relative position on the lines when the transversal cuts through them.3. Applying the Corresponding Angle Theorem: The Corresponding Angle Theorem states that when a transversal intersects two parallel lines, the corresponding angles are congruent. This means angle 2 and angle 6 are equal because they are corresponding angles.4. Completing the Proof: Therefore, the missing justification is Corresponding angles are congruent.

Answered by aiahbinilat | 2024-10-16