Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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.