prove
Given: line r is parallel to line s
prove: <1 is congruent to <2
To prove that angle <1 is congruent to angle <2, we need to show that they are corresponding angles formed by a transversal intersecting parallel lines.
Here's how you can prove it:
1. Draw a diagram: Draw two parallel lines, r and s. Label any two points on line r as A and B, and any two points on line s as C and D. Draw a transversal line that intersects lines r and s at points E and F, respectively.
A---------B <1
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E---------F <2
C---------D
2. Identify the corresponding angles: In this case, <1 and <2 are the angles formed by the transversal line EF that intersect line r and line s. From the diagram, you can see that <1 and <2 are corresponding angles.
3. State the given information: State that line r is parallel to line s. This is the given information in the problem.
4. Apply the properties of parallel lines: Use the property that when a transversal intersects two parallel lines, the corresponding angles formed are congruent. Therefore, since line r is parallel to line s and <1 and <2 are corresponding angles, <1 is congruent to <2.
5. Write the proof statement: Write a proof statement that concludes that <1 is congruent to <2 based on the given information and properties of parallel lines.
Proof:
Given: line r is parallel to line s
Statement 1: <1 and <2 are corresponding angles formed by a transversal (EF) intersecting lines r and s (definition of corresponding angles).
Statement 2: When a transversal intersects two parallel lines, the corresponding angles are congruent.
Statement 3: Therefore, <1 is congruent to <2 (conclusion based on statement 1 and 2).
Thus, we have proved that angle <1 is congruent to angle <2 based on the given information that line r is parallel to line s.