Pairs of Lines and Angles
Today you will need:
Grab a warm-up off the wooden desk and get started! :-)
Goals:
Warm-Up #1
Warm-Up #1 KEY
Linear Pair
Adjacent
Adjacent
Adjacent
Complementary
Adjacent
Adjacent
Linear Pair
Adjacent
Vertical Angles
Vertical Angles
Warm-Up #2
Warm-Up #2 KEY
x = 23
x = 20
x = 59
x = 8
Warm-up #1
Warm-up #2
Statements | Reasons |
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Warm-up #2
Statements | Reasons |
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Take notes! :-)
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. |
Angles formed by Transversals
Parallel Lines Cut by a Transversal
Practice!
Practice!
Practice!
Let’s Try some!
Log on to Student.desmos.com
100°
80°
100°
80°
80°
80°
100°
100°
Transversal will hit the same way in both parallel lines
Resources
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.
Warm-Up #1
Transversal
Dance, Dance