Geometry Chapter 3 3 6 PROVE THEOREMS ABOUT

Geometry Chapter 3 3 -6: PROVE THEOREMS ABOUT PERPENDICULAR LINES

Warm-Up

Prove Theorems about Perpendicular Lines Objective: Students will be able to prove properties of perpendicular lines, using them to solve problems. Agenda Theorems Proofs Example

For the Theorems List Theorem 3. 8: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

For the Theorems List Theorem 3. 9: If two lines are perpendicular, then they intersect to form four right angles.

Example 1

Example 1

For the Theorems List Theorem 3. 10: If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Example 2

Example 2

For the Theorems List Theorem 3. 11 – Perpendicular Transversal Theorem: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

For the Theorems List Theorem 3. 12 – 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.

Example 4: Drawing Conclusions from Diagrams

Example 4: Drawing Conclusions from Diagrams

Example 4: Drawing Conclusions from Diagrams

Example 4: Drawing Conclusions from Diagrams

Example 3: Drawing Conclusions from Diagrams From the given diagram, determine which lines, if any, must be parallel. Explain your reasoning using theorems as reference.

Distance from a line

Distance from a line

Example 5

Example 5

Example 5

Example 5 Step 3: Use the slope you just found to graph a perpendicular line that will go through the two lines.

Example 5

Example 5