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How Do You Prove Two Lines Are Parallel in Geometry?

Geometry is concerned mostly with shapes, size, properties of space and the relative position of certain figures. Parallel lines fall into the last category. By definition, parallel lines remain equidistant from each other and never cross. Geometry often makes use of postulates and theorems to prove or disprove relationships of figures. The easiest method to prove two lines are parallel in geometry is to apply postulate 12, which states that, "If two lines and a transversal form equal corresponding angles, then the lines are parallel."

Ruler
Protractor

Instructions

- 1
  Draw a transversal line between the two lines in question. A transversal line is simply a third line that intersects two or more lines in a plane. In essence, it is a slanted line drawn from just above the top line to just below the bottom line or from the left of the first line to right of the second line.
- 2
  Label the four angles formed by the first line and the transversal line 1 through 4. Label the first interior angle, the first angle that measures less than 90 degrees, No. 1 and continue the labeling process in a clockwise direction.
- 3
  Label the four angles formed by the second line and the transversal line 5 through 8. Label the angles in the same fashion as before, where the position of angle No. 5 on the second line corresponds to the position of angle No. 1 on the first line.
- 4
  Measure angle No. 1 and angle No. 5 with the protractor. If angle No. 1 is equal to angle No. 5, the two lines are parallel.

How to Factor Expressions With Common Factors

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