Section 3.6 – Prove Theorems About Perpendicular Lines

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Presentation transcript:

Section 3.6 – Prove Theorems About Perpendicular Lines

Section 3.6 – Prove Theorems About Perpendicular Lines Example 1: In the diagram below, Line AB is perpendicular to Line BC. What can you conclude about <1 and <2?

Section 3.6 – Prove Theorems About Perpendicular Lines

Section 3.6 – Prove Theorems About Perpendicular Lines Example 2: Prove that if two sides of two adjacent angles are perpendicular, then the angles are complementary. Given: Ray ED is perp to Ray EF Prove: <7 and <8 are complementary

Section 3.6 – Prove Theorems About Perpendicular Lines

Section 3.6 – Prove Theorems About Perpendicular Lines Example 3: Determine which lines, if any, must be parallel in the diagram. Explain you reasoning.

Section 3.6 – Prove Theorems About Perpendicular Lines Distance From a Line The distance from a point to a line is the length of the perpendicular segment from the point to the line. This perpendicular segment is the shortest distance between the point and the line. For example, the distance between point A and line k is AB.

Section 3.6 – Prove Theorems About Perpendicular Lines Distance From a Line The distance between two parallel lines is the length of any perpendicular segment joining the two lines. For example, the distance between line p and line m is CD or EF.

Section 3.6 – Prove Theorems About Perpendicular Lines Example 4: What is the distance from point A to line c? What is the distance from line c to line d?

Section 3.6 – Prove Theorems About Perpendicular Lines Example 5: Graph the line y = x + 1. What point on the line is the shortest distance from the point (4, 1)? What is the distance? Round to the nearest tenth.