Corresponding Angles Diagram Horizontal lines f and g are shown with a transversal line z that goes from the upper left to the lower right. Arrows on the lines f and g indicate that they are parallel. The intersection of lines f and z creates 4 angles. Angle 1 is in the upper left, angle 2 is in the upper right, angle 3 is in the lower left, and angle 4 is in the lower right. The intersection of lines g and z creates 4 angles. Angle 5 is in the upper left, angle 6 is in the upper right, angle 7 is in the lower left, and angle 8 is in the lower right. Question Multiple Choice Use the Corresponding Angles diagram to answer the question. Which can be used to directly prove that ? (1 point) Responses Alternate Interior Angles Theorem Alternate Interior Angles Theorem Corresponding Angles Postulate Corresponding Angles Postulate Same-Side Interior Angles Theorem Same-Side Interior Angles Theorem Alternate Exterior Angles Theorem
The correct answer is Corresponding Angles Postulate.
Based on the given diagram, the statement "Horizontal lines f and g are shown with a transversal line z that goes from the upper left to the lower right" suggests that lines f and g are parallel. Therefore, we can use the Corresponding Angles Postulate (Corresponding Angles Theorem) to directly prove that the corresponding angles formed by the intersection of lines f and z, and lines g and z are congruent.
So, the correct answer is: Corresponding Angles Postulate (Corresponding Angles Theorem).
To answer the question, we need to determine which theorem or postulate can be directly used to prove a particular relationship in the given diagram. The options given are:
1. Alternate Interior Angles Theorem
2. Corresponding Angles Postulate
3. Same-Side Interior Angles Theorem
4. Alternate Exterior Angles Theorem
To determine the correct answer, let's analyze the diagram:
The given diagram consists of two horizontal lines, f and g, which are indicated to be parallel. The transversal line z intersects both parallel lines, creating several angles.
Based on the diagram, we can observe that:
- Angles 3 and 5 are in the same position relative to the transversal and the parallel lines.
- Angles 1 and 7 are corresponding angles as they are on the same side of the transversal and they share the same position relative to the parallel lines.
Considering these observations, we can conclude that the correct answer is the "Corresponding Angles Postulate." The Corresponding Angles Postulate states that when two parallel lines are intersected by a transversal, the corresponding angles formed in the same relative position are equal.
Therefore, the Corresponding Angles Postulate can be directly used to prove the relationships of angles in this given diagram.