# Download 3.6 Prove Theorems about Perpendicular Lines

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Transcript
```Geometry Chapter 3: Parallel and Perpendicular Lines 3.6-­โ Prove Theorems about Perpendicular Lines SWBAT: find the distance between a point and a line. Common Core: G.GPE.5
โDo Nowโ
Write the following in Standard Form, then find the x & y intercepts.
2๐ฆ = 3๐ฅ โ 7
Theorem 3.8 If two lines intersect to form a linear pairs of congruent angles, then the lines are _____________________________________. If โ 1 โ โ 2, ๐กโ๐๐ ๐ โฅ โ.
Theorem 3.9 If two lines are perpendicular, then they intersect to form ___________________________________________. If ๐ โฅ ๐, ๐กโ๐๐ โ 1, โ 2, โ 3, โ 4 are
right angles.
Theorem 3. 10 If two sides of two adjacent acute angles are perpendicular, then the angles are _____________________________________. !!!!!โ โฅ ๐ต๐ถ
!!!!!โ , ๐กโ๐๐ โ 1 ๐๐๐ โ 2
If ๐ต๐ด
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 โ โฅ ๐ ๐๐๐ ๐ โฅ โ, then
๐ โฅ ๐.
Theorem 3.12 In a plane, if two lines are perpendicular to the same line, then they are ___________________________ to each other. If ๐ โฅ ๐ ๐๐๐ ๐ โฅ ๐ then
๐ โฅ ๐.
Example 1: In the diagram at the right โ 1 โ โ 2. What can you conclude about a and b? Example 2: In the diagram at the right, โ 1 โ โ 2. Prove that โ 3 ๐๐๐ โ 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 โ 196 #โs 3 โ 23 Odd and 39 โ 47 All ```
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