Standard #: MAFS.912.G-CO.3.9 (Archived Standard)


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.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: 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
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Items may assess relationships between vertical angles, special angles
    formed by parallel lines and transversals, angle bisectors, congruent
    supplements, congruent complements, and a perpendicular bisector
    of a line segment.

    Items may have multiple sets of lines and angles.

    Items may include narrative proofs, flow-chart proofs, two-column
    proofs, or informal proofs.

    In items that require the student to justify, the student should not be
    required to recall from memory the formal name of a theorem.

    Calculator :

    Neutral

    Clarification :
    Students will prove theorems about lines.

    Students will prove theorems about angles.

    Students will use theorems about lines to solve problems.

    Students will use theorems about angles to solve problems.

    Stimulus Attributes :
    Items may be set in a real-world or mathematical context. 
    Response Attributes :
    Items may require the student to give statements and/or
    justifications to complete formal and informal proofs.

    Items may require the student to justify a conclusion from a
    construction.



     



Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1

In the figure, begin mathsize 12px style stack A B with left right arrow on top space parallel to space stack C D with left right arrow on top space a n d space stack B C with left right arrow on top space parallel to space stack A E with left right arrow on top end style. Let begin mathsize 12px style angle A B D end style measure (3x+4)º, begin mathsize 12px style angle B C D end style measure(6x-8)º, and begin mathsize 12px style angle E D F end style measure (7x-20)º.

Click on the blank to enter the degree measure that completes the equation shown.

 

N/A EE: Equation Editor
Sample Item 2

Complete the proof by dragging the correct reasons to the table for line 3 and 6.

N/A DDHT: Drag-and-Drop Hot Text


Related Courses

Course Number1111 Course Title222
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))


Related Resources

Formative Assessments

Name Description
Proving the Corresponding Angles Theorem

Students are asked to prove that corresponding angles formed by the intersection of two parallel lines and a transversal are congruent.

Name That Triangle

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.

Finding Angle Measures - 1

Students are asked to find the measures of angles formed by three concurrent lines and to justify their answers.

Finding Angle Measures - 4

Students are asked to find the measure of an angle in a diagram containing two parallel lines and two transversals.

Finding Angle Measures - 3

Students are asked to find the measures of angles formed by two parallel lines and two transversals.

Finding Angle Measures - 2

Students are asked to find the measures of angles formed by two parallel lines and a transversal.

Proving the Alternate Interior Angles Theorem

In a diagram involving two parallel lines and a transversal, students are asked to use rigid motion to prove that alternate interior angles are congruent.

Equidistant Points

Students are asked to prove that a point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment.

Proving the Vertical Angles Theorem

Students are asked to identify a pair of vertical angles in a diagram and then prove that they are congruent.

Image/Photograph

Name Description
Angles (Clipart ETC) This large collection of clipart contains images of angles that can be freely used in lesson plans, worksheets, and presentations.

Lesson Plans

Name Description
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.

Parallel Thinking Debate

Students prove theorems related to parallel lines using vertical, corresponding, and alternate interior angles.

Vertical Angles: Proof and Problem-Solving

Students will explore the relationship between vertical angles and prove the Vertical Angle Theorem. They will use vertical angle relationships to calculate other angle measurements.

Proving and Using Congruence with Corresponding Angles

Students, will prove that corresponding angles are congruent. Directions for using GeoGebra software to discover this relationship is provided.

Determination of the Optimal Point

Students will use dynamic geometry software to determine the optimal location for a facility under a variety of scenarios. The experiments will suggest a relation between the optimal 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.

Parallel Lines

Students will prove that alternate interior angles and corresponding angles are congruent given two parallel lines and a traversal. Students will use GeoGebra to explore real-world images to prove their line segments are parallel.

Location, Location, Location, Location?

Students will use their knowledge of graphing concurrent segments in triangles to locate and identify which points of concurrency are associated by location with cities and counties within the Texas Triangle Mega-region.

Accurately Acquired Angles

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 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.

Detemination of the Optimal Point

Students will use dynamic geometry software to determine the optimal location for a facility under a variety of scenarios. The experiments will suggest a relation between the optimal 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.

Problem-Solving Tasks

Name Description
Points equidistant from two points in the plane

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.

Tangent Lines and the Radius of a Circle

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Tutorials

Name Description
Parallel lines and transversals

In this tutorial, students will find the measures of angles formed when a transversal cuts two parallel lines.

Parallel lines, transversals and triangles

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.

Parallel lines and transversal lines

Students will see in this tutorial the eight angles formed when two parallel lines are cut by a transversal line.

Parallel lines and transversals

In this tutorial, students will learn the angle measures when two parallel lines are cut by a transversal line.

Sum of Exterior Angles of an Irregular Pentagon

In this video, students will learn how to use what they know about the sum of angles in a triangle to determine the sum of the exterior angles of an irregular pentagon.

Proving 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.

Finding the measure of vertical angles

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.

Introduction to vertical angles

In this tutorial, students will use their knowledge of supplementary, adjacent, and vertical angles to solve problems involving the intersection of two lines.

Using Algebra to Find Measures of Angles Formed from Transversal

We will use algebra in order to find the measure of angles formed by a transversal.

Figuring Out Angles Between Transversal and Parallel Lines

We will be able to identify corresponding angles of parallel lines.

Angles Formed by Parallel Lines and Transversals

We will gain an understanding of how angles formed by transversals compare to each other.

Proof: Vertical Angles are Equal

This 5 minute video gives the proof that vertical angles are equal.

Student Resources

Problem-Solving Tasks

Name Description
Points equidistant from two points in the plane:

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.

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Tutorials

Name Description
Parallel lines and transversals:

In this tutorial, students will find the measures of angles formed when a transversal cuts two parallel lines.

Parallel lines, transversals and triangles:

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.

Parallel lines and transversal lines:

Students will see in this tutorial the eight angles formed when two parallel lines are cut by a transversal line.

Parallel lines and transversals:

In this tutorial, students will learn the angle measures when two parallel lines are cut by a transversal line.

Sum of Exterior Angles of an Irregular Pentagon:

In this video, students will learn how to use what they know about the sum of angles in a triangle to determine the sum of the exterior angles of an irregular pentagon.

Proving 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.

Finding the measure of vertical angles:

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.

Introduction to vertical angles:

In this tutorial, students will use their knowledge of supplementary, adjacent, and vertical angles to solve problems involving the intersection of two lines.

Using Algebra to Find Measures of Angles Formed from Transversal:

We will use algebra in order to find the measure of angles formed by a transversal.

Figuring Out Angles Between Transversal and Parallel Lines:

We will be able to identify corresponding angles of parallel lines.

Angles Formed by Parallel Lines and Transversals:

We will gain an understanding of how angles formed by transversals compare to each other.

Proof: Vertical Angles are Equal:

This 5 minute video gives the proof that vertical angles are equal.



Parent Resources

Problem-Solving Tasks

Name Description
Points equidistant from two points in the plane:

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.

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.



Printed On:3/28/2024 6:43:31 PM
Print Page | Close this window