Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Noether's theorem wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Perspective (graphical) wikipedia , lookup
History of geometry wikipedia , lookup
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 โDo Nowโ Write the following in Standard Form, then find the x & y intercepts. 2๐ฆ = 3๐ฅ 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, ๐กโ๐๐ ๐ โฅ โ. Theorem 3.9 If two lines are perpendicular, then they intersect to form ___________________________________________. If ๐ โฅ ๐, ๐กโ๐๐ 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 โฅ ๐ต๐ถ !!!!!โ , ๐กโ๐๐ โ 1 ๐๐๐ โ 2 If ๐ต๐ด 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 โฅ ๐ ๐๐๐ ๐ โฅ โ, then ๐ โฅ ๐. Theorem 3.12 In a plane, if two lines are perpendicular to the same line, then they are ___________________________ to each other. If ๐ โฅ ๐ ๐๐๐ ๐ โฅ ๐ then ๐ โฅ 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 3 ๐๐๐ 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 #โs 3 โ 23 Odd and 39 โ 47 All