Geometry Lines and Angles

GeometryLines and Angles CONFIDENTIAL

Warm Up Find the circumference and area of each circle. 1) 2) 80 cm 3.8 m CONFIDENTIAL

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

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 E F C D G H Parallel, perpendicular and skew lines CONFIDENTIAL

A B E F C D G H 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. CONFIDENTIAL

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 E F C D G H Parallel, perpendicular and skew lines CONFIDENTIAL

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

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

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 Referring to the figure, we can conclude: CONFIDENTIAL

C D B E G H F J Now you try! Identify each of the following: 1a) A pair of parallel segments 1b) A pair of skew segments 1c) A pair of perpendicular segments 1d) A pair of parallel planes CONFIDENTIAL

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

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

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

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

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

1 2 4 3 5 6 8 7 Classifying pairs of angles Give an example of each angle pair. 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

1 2 3 4 5 6 7 8 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 CONFIDENTIAL

4 l 1 2 3 5 6 n m Identifying angle pairs and transversals Identify the transversal and classify each angle pair. A) Angle 1 and angle 5 transversal: n;Alternate interior angles B) Angle 3 and angle 6 transversal: m;Correspondingangles C) Angle 1 and angle 4 transversal: l;Alternate exteriorangles CONFIDENTIAL

3) Identify the transversal and classify the angle pair 2 and 5 in the diagram. 4 l 1 2 3 5 6 m Now you try! n CONFIDENTIAL

B C A D F G E H Assessment Identify each of the following: 1) A pair of perpendicularsegments 2) A pair of skew segments 3) A pair of parallelsegments 4) A pair of parallel planes CONFIDENTIAL

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

m 1 2 n 4 5 3 p Identify the transversal and classify each angle pair. 9) Angle 1 and angle 2 10) Angle 2 and angle 3 11) Angle 2 and angle 4 12) Angle 4 and angle 5 CONFIDENTIAL

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 E F C D G H Let’s review Parallel, perpendicular and skew lines CONFIDENTIAL