Download 3.6 Prove Theorems about Perpendicular Lines

Geometry Chapter 3: Parallel and Perpendicular Lines 3.6-­‐ Prove Theorems about Perpendicular Lines SWBAT: find the distance between a point and a line. Common Core: G.GPE.5
“Do Now”
Write the following in Standard Form, then find the x & y intercepts.
2𝑦 = 3𝑥 − 7
Theorem 3.8 If two lines intersect to form a linear pairs of congruent angles, then the lines are _____________________________________. If ∠1 ≅ ∠2, 𝑡ℎ𝑒𝑛 𝑔 ⊥ ℎ.
Theorem 3.9 If two lines are perpendicular, then they intersect to form ___________________________________________. If 𝑎 ⊥ 𝑏, 𝑡ℎ𝑒𝑛 ∠1, ∠2, ∠3, ∠4 are
right angles.
Theorem 3. 10 If two sides of two adjacent acute angles are perpendicular, then the angles are _____________________________________. !!!!!⃗ ⊥ 𝐵𝐶
!!!!!⃗ , 𝑡ℎ𝑒𝑛 ∠1 𝑎𝑛𝑑 ∠2
If 𝐵𝐴
are complementary.
Geometry Chapter 3: Parallel and Perpendicular Lines Theorem 3.11 Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is ___________________________________ to the other. If ℎ ∥ 𝑘 𝑎𝑛𝑑 𝑗 ⊥ ℎ, then
𝑗 ⊥ 𝑘.
Theorem 3.12 In a plane, if two lines are perpendicular to the same line, then they are ___________________________ to each other. If 𝑚 ⊥ 𝑝 𝑎𝑛𝑑 𝑛 ⊥ 𝑝 then
𝑚 ∥ 𝑛.
Example 1: In the diagram at the right ∠1 ≅ ∠2. What can you conclude about a and b? Example 2: In the diagram at the right, ∠1 ≅ ∠2. Prove that ∠3 𝑎𝑛𝑑 ∠4 are complementary. Geometry Chapter 3: Parallel and Perpendicular Lines Example 3: Determine which lines, if any, must be parallel in the diagram. Explain your reasoning. Example : Determine which lines, if any, must be parallel in the diagram. Explain your reasoning. Geometry Chapter 3: Parallel and Perpendicular Lines Example 4: Find the distance between two parallel lines The section of broad gauge railroad track are drawn on a graph where units are measured in inches. What is the width of the track? Geometry Chapter 3: Parallel and Perpendicular Lines Example: Use the graph at the right for Exercises 5 and 6. 5. What is the distance from point A to line c? Homework: Pgs. 194 – 196 #’s 3 – 23 Odd and 39 – 47 All