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Standard #: MAFS.912.G-CO.3.9
This document was generated on CPALMS - www.cpalms.org
Prove theorems about lines and angles; use theorems about lines and angles to solve problems.
Theorems include: 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.
Subject Area: Mathematics
Grade: 912
Domain: Geometry: Congruence
Cluster: Prove geometric theorems - Geometry - Major Cluster
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More
Information
Date of Last Rating: 02/14
Status: State Board Approved
Related Courses
Course Number
1206315:
1206310:
1206320:
Course Title
Geometry for Credit Recovery (Specifically in versions: 2014 2015, 2015 and beyond (current))
Geometry (Specifically in versions: 2014 - 2015, 2015 and
beyond (current))
Geometry Honors (Specifically in versions: 2014 - 2015, 2015
and beyond (current))
7912065:
1200400:
Access Geometry (Specifically in versions: 2015 and beyond
(current))
Intensive Mathematics (Specifically in versions: 2014 - 2015,
2015 and beyond (current))
Related Access Points
Access Point
Access Point Number
MAFS.912.G-CO.3.AP.9a
Access Point Title
Measure lengths of line segments and angles to establish the
facts about the angles created when parallel lines are cut by a
transversal and the points on a perpendicular bisector.
Related Resources
Lesson Plan
Name
Description
Students will start the lesson by playing a game to review angle
pairs formed by two lines cut by a transversal. Once students are
comfortable with the angle pairs the teacher will review the
relationships that are created once the pair of lines become
parallel. The teacher will give an example of a proof using the
Accurately Acquired Angles angle pairs formed by two parallel lines cut by a transversal.
The students are then challenged to prove their own theorem in
groups of four. The class will then participate in a Stay and
Stray to view the other group's proofs. The lesson is wrapped up
through white board questions answered within groups and then
as a whole class.
Students will use dynamic geometry software to determine the
optimal location for a facility under a variety of scenarios. The
Detemination of the Optimal experiments will suggest a relation between the optimal point
Point
and a common concept in geometry; in some cases, there will be
a connection to a statistical concept. Algebra can be used to
verify some of the conjectures.
Students will use dynamic geometry software to determine the
optimal location for a facility under a variety of scenarios. The
Determination of the Optimal
experiments will suggest a relation between the optimal point
Point (formerly where to build
and a common concept in geometry; in some cases, there will be
a house)
a connection to a statistical concept. Algebra can be used to
verify some of the conjectures.
Engineering Design
Challenge: Exploring
Structures in High School
Geometry
Students explore ideas on how civil engineers use triangles
when constructing bridges. Students will apply knowledge of
congruent triangles to build and test their own bridges for
stability.
Students will use their knowledge of graphing concurrent
Location, Location, Location, segments in triangles to locate and identify which points of
Location?
concurrency are associated by location with cities and counties
within the Texas Triangle Mega-region.
Students will be able to prove that alternate interior angles are
congruent and corresponding angles are congruent given two
Parallel Lines
parallel lines and a traversal line. Students will use GeoGebra to
explore real-world images to see if they can prove that their line
segments are parallel.
Students prove theorems related to parallel lines using vertical,
Parallel Thinking Debate
corresponding, and alternate interior angles.
Proving and Using
Students, with the aid of GeoGebra software, will prove and use
Congruence with
congruence of corresponding angles produced by parallel lines
Corresponding Angles
intersected by a traversal.
In this lesson, students learn about the relationship between
vertical angles by making inferences and proving the Vertical
Vertical Angles: Proof and
Angle Theorem. They then use this relationship to prove other
Problem-Solving
angle relationships and to find angle measurements by using
vertical angles.
Image/Photograph
Name
Angles (Clipart ETC)
Description
This large collection of clipart contains images of angles that
can be freely used in lesson plans, worksheets, and
presentations.
Tutorial
Name
Angles Formed by Parallel
Lines and Transversals
Figuring Out Angles Between
Transversal and Parallel Lines
Finding the measure of
vertical angles
Description
We will gain an understanding of how angles formed by
transversals compare to each other.
We will be able to identify corresponding angles of parallel
lines.
Students will use algebra to find the measure of vertical angles,
or angles opposite each other when two lines cross. Students
should have an understanding of complementary and
supplementary angles before viewing this video.
In this tutorial, students will use their knowledge of
Introduction to vertical angles supplementary, adjacent, and vertical angles to solve problems
involving the intersection of two lines.
Parallel lines and transversal Students will see in this tutorial the eight angles formed when
lines
two parallel lines are cut by a transversal line.
In this tutorial, students will learn the angle measures when two
Parallel lines and transversals
parallel lines are cut by a transversal line.
In this tutorial, students will find the measures of angles formed
Parallel lines and transversals
when a transversal cuts two parallel lines.
This tutorial shows students the eight angles formed when two
parallel lines are cut by a transversal line. There is also a
Parallel lines, transversals and
review of triangles in this video.
triangles
Proof: Vertical Angles are
Equal
This 5 minute video gives the proof that vertical angles are
equal.
In this tutorial, students prove that vertical angles are
Proving vertical angles are
equal. Students should have an understanding of supplementary
equal
angles before viewing this video.
In this video, students will learn how to use what they know
Sum of Exterior Angles of an
about the sum of angles in a triangle to determine the sum of the
Irregular Pentagon
exterior angles of an irregular pentagon.
Using Algebra to Find
We will use algebra in order to find the measure of angles
Measures of Angles Formed
formed by a transversal.
from Transversal
Formative Assessment
Name
Equidistant Points
Finding Angle Measures - 1
Finding Angle Measures - 2
Finding Angle Measures - 3
Finding Angle Measures - 4
Name That Triangle
Description
Students are asked to prove that a point on the perpendicular
bisector of a line segment is equidistant from the endpoints of
the segment.
Students are asked to find the measures of angles formed by
three concurrent lines and to justify their answers.
Students are asked to find the measures of angles formed by two
parallel lines and a transversal.
Students are asked to find the measures of angles formed by two
parallel lines and two transversals.
Students are asked to find the measure of an angle in a diagram
containing two parallel lines and two transversals.
Students are asked to describe a triangle whose vertices are the
endpoints of a segment and a point on the perpendicular bisector
of a segment.
In a diagram involving two parallel lines and a transversal,
Proving the Alternate Interior
students are asked to use rigid motion to prove that alternate
Angles Theorem
interior angles are congruent.
Proving the Vertical Angles Students are asked to identify a pair of vertical angles in a
Theorem
diagram and then prove that they are congruent.
Educational Game
Name
Description
Play a game to discover the relationship between opposite
angles and identify names of angles by their measures. Students
may select Teach Me to learn about these angle relationships
prior to beginning play. Hints and feedback are provided to
players.
Opposite Angles
Problem-Solving Task
Name
Description
This task asks students to show how certain points on a plane
Points equidistant from two
are equidistant to points on a segment when placed on a
points in the plane
perpendicular bisector.
This problem solving task challenges students to find the
Tangent Lines and the Radius
perpendicular meeting point of a segment from the center of a
of a Circle
circle and a tangent.
Assessment
Name
Sample 2 - High School
Geometry State Interim
Assessment
Sample 3 - High School
Geometry State Interim
Assessment
Description
This is a State Interim Assessment for 9th-12th grade.
This is a State Interim Assessment for 9th-12th grade.
Student Resources
Name
Angles Formed by
Parallel Lines and
Transversals
Description
We will gain an understanding of how angles formed by
transversals compare to each other.
Figuring Out Angles
Between Transversal
and Parallel Lines
Finding the measure
of vertical angles
Introduction to
vertical angles
Opposite Angles
Parallel lines and
transversal lines
Parallel lines and
transversals
Parallel lines and
transversals
Parallel lines,
transversals and
triangles
Points equidistant
from two points in the
plane
Proof: Vertical Angles
are Equal
We will be able to identify corresponding angles of parallel lines.
Students will use algebra to find the measure of vertical angles, or
angles opposite each other when two lines cross. Students should have
an understanding of complementary and supplementary angles before
viewing this video.
In this tutorial, students will use their knowledge of supplementary,
adjacent, and vertical angles to solve problems involving the
intersection of two lines.
Play a game to discover the relationship between opposite angles and
identify names of angles by their measures. Students may select Teach
Me to learn about these angle relationships prior to beginning
play. Hints and feedback are provided to players.
Students will see in this tutorial the eight angles formed when two
parallel lines are cut by a transversal line.
In this tutorial, students will learn the angle measures when two parallel
lines are cut by a transversal line.
In this tutorial, students will find the measures of angles formed when a
transversal cuts two parallel lines.
This tutorial shows students the eight angles formed when two parallel
lines are cut by a transversal line. There is also a review of triangles in
this video.
This task asks students to show how certain points on a plane are
equidistant to points on a segment when placed on a perpendicular
bisector.
This 5 minute video gives the proof that vertical angles are equal.
In this tutorial, students prove that vertical angles are equal. Students
should have an understanding of supplementary angles before viewing
this video.
Sum of Exterior
In this video, students will learn how to use what they know about the
Angles of an Irregular sum of angles in a triangle to determine the sum of the exterior angles
Pentagon
of an irregular pentagon.
Tangent Lines and the This problem solving task challenges students to find the perpendicular
Radius of a Circle
meeting point of a segment from the center of a circle and a tangent.
Using Algebra to Find
Measures of Angles We will use algebra in order to find the measure of angles formed by a
Formed from
transversal.
Transversal
Proving vertical
angles are equal
Parent Resources
Name
Points equidistant
from two points in the
plane
Tangent Lines and the
Radius of a Circle
Description
This task asks students to show how certain points on a plane are
equidistant to points on a segment when placed on a perpendicular
bisector.
This problem solving task challenges students to find the perpendicular
meeting point of a segment from the center of a circle and a tangent.