1 of 23

Pairs of Lines and Angles

Today you will need:

  1. Notes
  2. Chromebook
  3. Positive Attitude! :-)

Grab a warm-up off the wooden desk and get started! :-)

2 of 23

Goals:

  • Develop understanding of angle relationships formed by transversals.

3 of 23

Warm-Up #1

4 of 23

Warm-Up #1 KEY

Linear Pair

Adjacent

Adjacent

Adjacent

Complementary

Adjacent

Adjacent

Linear Pair

Adjacent

Vertical Angles

Vertical Angles

5 of 23

Warm-Up #2

6 of 23

Warm-Up #2 KEY

x = 23

x = 20

x = 59

x = 8

7 of 23

Warm-up #1

8 of 23

Warm-up #2

Statements

Reasons

9 of 23

Warm-up #2

Statements

Reasons

10 of 23

Take notes! :-)

11 of 23

New Vocabulary: Sketch a Diagram

Parallel Lines: Two lines are parallel lines when they do not intersect and are coplanar.

Skew Lines: Two lines are skew lines when they do not intersect and are not coplanar.

Parallel Planes: Two planes that do not intersect are parallel planes.

Transversal: A line that passes through two lines in the same plane at two distinct points.

12 of 23

Angles formed by Transversals

13 of 23

Parallel Lines Cut by a Transversal

14 of 23

Practice!

15 of 23

Practice!

16 of 23

Practice!

17 of 23

Let’s Try some!

18 of 23

Log on to Student.desmos.com

19 of 23

100°

80°

100°

80°

80°

80°

100°

100°

Transversal will hit the same way in both parallel lines

20 of 23

Resources

21 of 23

Mod 2 Standards

G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, eg. using the distance formula.

G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted to the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

G.GPE.4 Use coordinates to prove simple geometric theorems algebraically and to verify geometric relationships algebraically, including properties of special triangles, quadrilaterals, and circles. For example, determine if a figure defined by four given points in the coordinate plane is a rectangle; determine if a specific point lies on a given circle.

G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using items such as graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G.CO.3ab Identify the symmetries of a figure, which are the rotations and reflections that carry it onto itself.�a. Identify figures that have line symmetry; draw and use lines of symmetry to analyze properties of shapes.�b. Identify figures that have rotational symmetry; determine the angle of rotation, and use rotational symmetry to analyze properties of shapes.

G.CO.10 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

22 of 23

Warm-Up #1

23 of 23

Transversal

Dance, Dance