Perpendicular Parallel linestheorem.pptx

Grade 8 Mathematics Parallel and Perpendicular Lines Theorem
Ma'am Rose Grade 8 Mathematics
Theorems of Parallel and Theorems of Perpendicular

1. MATHEMATICS 8 PARALLEL PERPENDICULAR LINES THEOREM

2. L ine A line goes on and on in both directions. A line is drawn with an arrow on each end .

3. Point This is called a point! When it’s at the end of a line it is called an endpoint!

4. L ine Segment A line segment is a part of a line. It is drawn with two endpoints

5. Ray A ray goes on and on in one direction. It is drawn with an arrow on one end and an endpoint on the other.

6. Two coplanar lines that have a point in common. INTERSECTING LINES CONCURRENT LINES PERPENDICULAR LINES A Two intersecting lines meeting at point A. Three or more coplanar lines that intersect at exactly one point. Concurrent lines meeting at a point O. Two lines that intersect and form a right angle. O A B C D E EC ⊥ AB “ray EC is perpendicular to line AB

7. Parallel lines Parallel lines are always the same distance apart. They will never touch. “Enemy Lines”

8. Parallel lines Can you find the parallel lines?

9. Parallel lines Parallel lines are any two coplanar lines that do not intersect A B D C AB ∥ CD symbol for parallelism

10. Parallel Postulate There is exactly one line parallel to a line at a given point not contained on a line.

11. Intersecting lines Intersecting lines are two lines that cross each other “Friends”

12. Intersecting lines Can you find the intersecting lines?

13. Perpendicular lines 90 Perpendicular lines are two lines that intersect to form right angles. “Married”

14. Perpendicular lines Can you find the perpendicular lines?

15. Perpendicular lines Perpendicular lines are also intersecting lines because they cross each other. Perpendicular lines are a special kind of intersecting lines because they always form “perfect” right angles.

16. Perpendicular lines Perpendicular lines are the two intersecting lines that form right angles A B C D AB ⊥ CD symbol for perpendicularity

17. Theorems of Perpendicular lines 1. If two lines are perpendicular to each other, then they form four right angles. n m 1 2 3 4 If m ⊥ n , then we can conclude that ∠ 1, ∠ 2, ∠ 3, and ∠ 4 are right angles.

18. Theorems of Perpendicular lines 2. If the angles in a linear pair are congruent, then the lines containing their sides are perpendicular n m 1 2 3 4 If ∠ 1 and ∠ 2 form a linear pair and ∠ 1 ≅ ∠ 2, then m ⊥ n

19. Theorems of Perpendicular lines 3. If two angles are adjacent and complementary, the non-common sides are perpendicular. C If ∠ CAR and ∠ EAR are complementary and adjacent, then AC ⊥ AE. A R E

20. Examples

21. Examples 2x + 20 = 90 2x = 90 – 20 2x = 70 2 x = 35

22. Try This !

23. l m n p q Name all possible pairs of: Parallel lines Perpendicular lines m ⃦ n p ⃦ q l ⊥ p l ⊥ q

24. L I K E Name all possible pairs of: Parallel lines Perpendicular lines LI ⃦ EK LE ⃦ I K LI ⊥ LE IL ⊥ IK KI ⊥ KE EL ⊥ EK

25. Geography Way History Lane Science Avenue Math Avenue Algebra Street Geometry Street Main Street English Street Prehistoric Place

26. 1. Science Avenue is parallel to? a. Geometry Street b. English Street c. Geography Way d. Math Avenue PARALLEL TOWN

27. 1. Science Avenue is parallel to? a. Geometry Street b. English Street c. Geography Way d. Math Avenue PARALLEL TOWN

28. 2. Science Avenue is perpendicular to? a. Math Avenue b. Geography Way c. Algebra Street d. English Street PARALLEL TOWN

29. 2. Science Avenue is perpendicular to? a. Math Avenue b. Geography Way c. Algebra Street d. English Street PARALLEL TOWN

30. 3. Science Avenue and Geometry Street are________roads ? Parallel Perpendicular Intersecting PARALLEL TOWN

31. 3. Science Avenue and Geometry Street are________roads ? Parallel Perpendicular Intersecting PARALLEL TOWN

32. 4. Geometry Street are perpendicular to? History Lane Main Street Prehistoric Place Geography Way PARALLEL TOWN

33. 4. Geometry Street are perpendicular to? History Lane Main Street Prehistoric Place Geography Way PARALLEL TOWN

34. 5. History Lane and Prehistoric Place are_______roads ? Parallel Intersecting Perpendicular PARALLEL TOWN

35. 5. History Lane and Prehistoric Place are_______roads ? Parallel Intersecting Perpendicular PARALLEL TOWN