1. Geometry Lines and Angles
CONFIDENTIAL

2. Find the circumference and area of each circle.
Warm Up
Find the circumference and area of each circle. 1) 2)
80 cm
3.8 m
1) P=502.4 cm;
A =20096 cm2
2) P= m;
A = m2
CONFIDENTIAL

3. Parallel, perpendicular and skew lines
Pairs of lines can relate to each other in four different ways: intersecting lines, parallel lines, perpendicular lines and skew lines. These concepts are useful for understanding and solving various geometry problems.
CONFIDENTIAL

4. Parallel, perpendicular and skew lines
Parallel lines (||) are lines that never intersect i.e. they are coplanar. The distance between the two lines is fixed and the two lines go in the same direction.
In the figure, AB || EF and EG || FH. A B C D E F G H
CONFIDENTIAL

5. Parallel, perpendicular and skew lines
Perpendicular lines (|)are lines that intersect at one point and form a 90° angle i.e. two different straight lines on the same plane in two different directions who meet each other at only right angles are called Perpendicular Lines.
In the figure, AB | AE and EG | GH. A B C D E F G H
CONFIDENTIAL

6. Parallel, perpendicular and skew lines
Skew lines are not coplanar. Skew lines only happen in space. Skew lines never intersect because they are not on the same plane. Skew lines are difficult to draw because they exist in the three dimensional space.
In the figure, AB and EG are skew. A B C D E F G H
CONFIDENTIAL

7. Parallel, perpendicular and skew lines
Parallel planes are planes that do not intersect.
In the figure, plane ABE || plane CDG. A B C D E F G H
CONFIDENTIAL

8. Identifying types of lines and planes
Identify each of the following:
A pair of parallel segments.
KN || PS K L P Q N M S R
B) A pair of skew segments.
LM || RS
C) A pair of perpendicular segments.
MR | RS
D) A pair of parallel planes.
plane KPS || plane LQR.
CONFIDENTIAL

9. Referring to the figure, we can conclude:
AB is perpendicular to CL and  CIB is 90°
KE intersects IB at point J
GH is parallel to AB
KD is perpendicular to MH and  KLH is 90°
IL intersects JM at point K
EF intersects GL at point M, intersects IL at point K and IB at point J
CONFIDENTIAL

10. Identify each of the following:
Now you try!
Identify each of the following: C D G H B E F J
1a) A pair of parallel segments
1b) A pair of skew segments
1c) A pair of perpendicular segments
1d) A pair of parallel planes
1a) CD || BE
1b) BE and EJ are skew
1c) BC | CD
1d) plane BCD || plane FGH
CONFIDENTIAL

11. Angle pairs formed by a transversal
A transversal is a line that intersects two coplanar lines at two different points. The traversal t and the other two lines r and s form eight angles.
exterior angles
interior angles
exterior angles
CONFIDENTIAL

12. Corresponding angles are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection i.e. angle 1 and angle 5.
Corresponding angles
CONFIDENTIAL

13. Alternate interior angles
Alternate interior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal i.e. angle 3 and angle 5.
Alternate interior angles
CONFIDENTIAL

14. Alternate exterior angles
Alternate exterior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal i.e. angle 1 and angle 7.
Alternate exterior angles
CONFIDENTIAL

15. Same side interior angles
Same side interior angles crosses two (usually parallel) lines. Each pair of interior angles are inside the parallel lines, and on the same side of the transversal. i.e. angle 3 and angle 6.
Same side interior angles
CONFIDENTIAL

16. Classifying pairs of angles
Give an example of each angle pair.
4 3
1 2
8 7
5 6
A) Corresponding angles
Angle 4 and angle 8
B) Alternate interior angles
Angle 4 and angle 6
C) Alternate exterior angles
Angle 2 and angle 8
D) Same side interior angles
Angle 4 and angle 5
CONFIDENTIAL

17. Give an example of each angle pair.
Now you try!
Give an example of each angle pair.
2a) Corresponding angles
2b) Alternate interior angles
2c) Alternate exterior angles
2d) Same side interior angles
2a) Angle 6 and angle 8
2b) Angle 6 and angle 3
2c) Angle 4 and angle 5
2d) Angle 2 and angle 3
CONFIDENTIAL

18. Identifying angle pairs and transversals
Identify the transversal and classify each angle pair.
A) Angle 1 and angle 5
transversal: n; Alternate interior angles 4 5 6 m l n
B) Angle 3 and angle 6
transversal: m; Corresponding angles
C) Angle 1 and angle 4
transversal: l; Alternate exterior angles
CONFIDENTIAL

19. 3) transversal: n; Same side interior angles
Now you try!
3) Identify the transversal and classify the angle pair 2 and 5 in the diagram. 4 5 6 m l n
3) transversal: n; Same side interior angles
CONFIDENTIAL

20. BREAK
CONFIDENTIAL

21. Click on the link below for some exciting puzzle
GAME
Click on the link below for some exciting puzzle
CONFIDENTIAL

22. Identify each of the following:
Assignments
Identify each of the following: B C F G A D E H
1) A pair of perpendicular segments
2) A pair of skew segments
3) A pair of parallel segments
4) A pair of parallel planes
1a) CD || BE
1b) BE and EJ are skew
1c) BC | CD
1d) plane BCD || plane FGH
CONFIDENTIAL

23. Give an example of each angle pair.
5) Alternate interior angles
6) Alternate exterior angles
7) Corresponding angles
8) Same side interior angles
5) Angle 3 and angle 1
6) Angle 5 and angle 7
7) Angle 4 and angle 5
8) Angle 2 and angle 3
CONFIDENTIAL

24. Identify the transversal and classify each angle pair. 3 5 4 m n p
9) Angle 1 and angle 2
10) Angle 2 and angle 3
11) Angle 2 and angle 4
12) Angle 4 and angle 5
9) transversal: p; Corresponding angles
10) transversal: m; Alternate exterior angles
11) transversal: n; Alternate angles
12) transversal: n; Same side interior angles
CONFIDENTIAL

25. Parallel, perpendicular and skew lines
Let’s review
Parallel, perpendicular and skew lines
Parallel lines (||) are lines that never intersect i.e. they are coplanar. The distance between the two lines is fixed and the two lines go in the same direction.
In the figure, AB || EF and EG || FH. A B C D E F G H
CONFIDENTIAL

26. Parallel, perpendicular and skew lines
Perpendicular lines (|)are lines that intersect at one point and form a 90° angle i.e. two different straight lines on the same plane in two different directions who meet each other at only right angles are called Perpendicular Lines.
In the figure, AB | AE and EG | GH. A B C D E F G H
CONFIDENTIAL

27. Parallel, perpendicular and skew lines
Skew lines are not coplanar. Skew lines only happen in space. Skew lines never intersect because they are not on the same plane. Skew lines are difficult to draw because they exist in the three dimensional space.
In the figure, AB and EG are skew. A B C D E F G H
CONFIDENTIAL

28. Parallel, perpendicular and skew lines
Parallel planes are planes that do not intersect.
In the figure, plane ABE || plane CDG. A B C D E F G H
CONFIDENTIAL

29. Angle pairs formed by a transversal
A transversal is a line that intersects two coplanar lines at two different points. The traversal t and the other two lines r and s form eight angles.
exterior angles
interior angles
exterior angles
CONFIDENTIAL

30. Corresponding angles are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection i.e. angle 1 and angle 5.
Corresponding angles
CONFIDENTIAL

31. Alternate interior angles
Alternate interior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal i.e. angle 3 and angle 5.
Alternate interior angles
CONFIDENTIAL

32. Alternate exterior angles
Alternate exterior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal i.e. angle 1 and angle 7.
Alternate exterior angles
CONFIDENTIAL

33. Same side interior angles
Same side interior angles crosses two (usually parallel) lines. Each pair of interior angles are inside the parallel lines, and on the same side of the transversal. i.e. angle 3 and angle 6.
Same side interior angles
CONFIDENTIAL

34. You did a great job today!
CONFIDENTIAL