3.6 Prove Theorems About Perpendicular Lines

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Presentation transcript:

3.6 Prove Theorems About Perpendicular Lines 3.6 Proving Theorems about Perpendicular Lines 3.6 Prove Theorems About Perpendicular Lines Objectives: To find the distance from a point to a line To prove theorems about perpendicular lines

Example 1 What is the distance from point P to line l?

Example 2 What is the shortest distance from P to line l?

Distance from a Point to a Line The distance from a point to a line is the length of the perpendicular segment from the point to the line. This is the shortest distance from the point to the line.

Distance Between Parallel Lines Likewise, the distance between two parallel lines is the length of any perpendicular segment joining the two lines.

Example 3 Find the distance from (-4, 3) to the line

Distance from a Point to a Line The distance from a point (x1, y1) to the line Ax + By + C = 0 is given by the formula Ax + By + C = 0

Example 4 Find the distance from (-4, 3) to the line

The Proof Game! Here’s your chance to play the game that is quickly becoming a favorite among America’s teenagers: The Proof Game! In this game, your group will be given one theorem. You are to collaborate with your group members to prove this theorem. Then you must choose someone to present said proof to the class. That presenter will earn a delicious reward!

Theorems Galore! If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

Theorems Galore! If two lines are perpendicular, then they intersect to form four right angles.

Theorems Galore! If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Theorems Galore! Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. j

Theorems Galore! Lines Perpendicular to a Transversal Theorem In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

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