Q4W5.lines and segment are perpendicular

Determining the conditions under which lines and segments are perpendicular

1. DETERMINING THE CONDITIONS UNDER WHICH LINES AND SEGMENTS ARE PERPENDICULAR Quarter 4 – Week 5

2. Objectives: At the end of the discussion, the students will be able to: Identify the properties of parallel lines and perpendicular lines; Prove the conditions under which lines and segments are parallel or perpendicular: and Apply properties of parallel and perpendicular lines to real life situations.

3. Statements Reasons ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Given m∠1= m∠2 Definition of Right Angles m∠2= 90° g ⊥ h

4. Statements Reasons ∠1 and ∠2 are linear pair Given Definition of Supplementary m∠1+ m∠2 = 180° Given m∠1= m∠2 Definition of Right Angles m∠2= 90° g ⊥ h

5. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Given m∠1= m∠2 Definition of Right Angles m∠2= 90° g ⊥ h

6. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Definition of Linear Pair Given m∠1= m∠2 Definition of Right Angles m∠2= 90° g ⊥ h

7. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Definition of Linear Pair ∠1 ≅ ∠2 Given m∠1= m∠2 Definition of Right Angles m∠2= 90° g ⊥ h

8. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Definition of Linear Pair ∠1 ≅ ∠2 Given m∠1= m∠2 Definition of Congruent Angles Definition of Right Angles m∠2= 90° g ⊥ h

9. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Definition of Linear Pair ∠1 ≅ ∠2 Given m∠1= m∠2 Definition of Congruent Angles m∠1= 90° Definition of Right Angles m∠2= 90° g ⊥ h

10. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Definition of Linear Pair ∠1 ≅ ∠2 Given m∠1= m∠2 Definition of Congruent Angles m∠1= 90° Definition of Right Angles m∠2= 90° Definition of Right Angles g ⊥ h

11. Statements Reasons ∠1 and ∠2 are linear pair Given ∠1 and ∠2 are linear pair Definition of Supplementary m∠1+ m∠2 = 180° Definition of Linear Pair ∠1 ≅ ∠2 Given m∠1= m∠2 Definition of Congruent Angles m∠1= 90° Definition of Right Angles m∠2= 90° Definition of Right Angles g ⊥ h Definition of Perpendicular Line

12. Statements Reasons b ⊥ a ∠1 is a right angle m∠1= 90° m∠4= 90° ∠1 and ∠2 are linear pair m∠1+ m∠2 = 180° m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

13. Statements Reasons b ⊥ a Given ∠1 is a right angle m∠1= 90° m∠4= 90° ∠1 and ∠2 are linear pair m∠1+ m∠2 = 180° m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

14. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° m∠4= 90° ∠1 and ∠2 are linear pair m∠1+ m∠2 = 180° m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

15. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° ∠1 and ∠2 are linear pair m∠1+ m∠2 = 180° m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

16. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° Vertical Angle are Congruent ∠1 and ∠2 are linear pair m∠1+ m∠2 = 180° m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

17. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° Vertical Angle are Congruent ∠1 and ∠2 are linear pair Given m∠1+ m∠2 = 180° m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

18. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° Vertical Angle are Congruent ∠1 and ∠2 are linear pair Given m∠1+ m∠2 = 180° Definition of Linear Pair m∠2 = 90° m∠3 = 90° ∠3, and ∠4 are right angles.

19. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° Vertical Angle are Congruent ∠1 and ∠2 are linear pair Given m∠1+ m∠2 = 180° Definition of Linear Pair m∠2 = 90° Definition of Right Angle m∠3 = 90° ∠3, and ∠4 are right angles.

20. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° Vertical Angle are Congruent ∠1 and ∠2 are linear pair Given m∠1+ m∠2 = 180° Definition of Linear Pair m∠2 = 90° Definition of Right Angle m∠3 = 90° Vertical Angle Theorem ∠3, and ∠4 are right angles.

21. Statements Reasons b ⊥ a Given ∠1 is a right angle Definition of Perpendicular Lines m∠1= 90° Definition of Right Angle m∠4= 90° Vertical Angle are Congruent ∠1 and ∠2 are linear pair Given m∠1+ m∠2 = 180° Definition of Linear Pair m∠2 = 90° Definition of Right Angle m∠3 = 90° Vertical Angle Theorem ∠3, and ∠4 are right angles. Definition of Right Angle / Perpendicular Lines

22. Right angles are congruent

23. Right angles are congruent

24. Right angles are congruent

25. Right angles are congruent

26. Right angles are congruent

27. Right angles are congruent

28. Right angles are congruent

29. Right angles are congruent

30. LET US TRY!

31. Can you identify what I am?

32. Can you identify what I am? Antenna

33. If two lines intersect to form a _____ of congruent angles, then the lines are perpendicular. If two lines are ______, then they intersect to form four right angles. If a transversal is perpendicular to one of two ______ lines, then it is perpendicular to the other. In a plane, if two lines are perpendicular to the ____ line, then they are parallel to each other. Sum it up!

34. Prove the given using two-column proof.

35. —Rico M. Villalon “Thank You for listening!”