EngageNY
Secant Lines; Secant Lines That Meet Inside a Circle
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
EngageNY
Segments That Meet at Right Angles
Can segments be considered perpendicular if they don't intersect? Learners look at nonintersecting segments on the coordinate plane and make conclusions about the lines that contain those segments. They determine if they are...
Curated OER
Parallel and Perpendicular Lines and Lines of Symmetry: Rhombus Shadowing
Fifth graders demonstrate different types of lines using movement. In this line and movement lesson, 5th graders demonstrate parallel and perpendicular lines, and lines of symmetry using dance movement. They also demonstrate rhombus...
EngageNY
Characteristics of Parallel Lines
Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...
EngageNY
Lines That Pass Through Regions
Good things happen when algebra and geometry get together! Continue the exploration of coordinate geometry in the third lesson in the series. Pupils explore linear equations and describe the points of intersection with a given polygon as...
Curated OER
Identifying Linear Functions from Graphs
Keep your mathematicians engaged using this group linear functions activity. Each of ten groups receives two graphs with both an image and equation, as well as a "who has" phrase to call out the next graph. Scholars stay on their toes as...
West Contra Costa Unified School District
Parallel Lines Cut by a Transversal
Parallel lines seem so right for each other. It's too bad they'll never, ever meet. Learners use tracing paper to discover relationships among angles formed by two parallel lines cut by a transversal. They apply this information to find...
EngageNY
Looking More Carefully at Parallel Lines
Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...
Curated OER
Sample Lesson Plan on Lines and Angles
Student complete worksheet using the definitions of lines and angle vocabulary. They define the word and follow a direction given on the worksheet such "construct a line." They complete an online tutorial on how to measure angles using a...
EngageNY
Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams
First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
Willow Tree
Angles Formed by Transversals of Coplanar Lines
Create a strong understanding of the relationships formed when parallel lines intersect a transversal. Discuss each type of angle pair and their relationship to each other.
Illustrative Mathematics
Equations of Lines
The intent of this resource is to show algebra learners that there is a proportional relationship between two lines that have an intersecting point. As the coordinate x increases by a constant, the y coordinate also increases. It will...
EngageNY
Secant Angle Theorem, Exterior Case
It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous instructional activity to investigate angles created by secant lines that intersect at a point exterior to...
Illustrative Mathematics
The Intersection of Two Lines
Here is an introduction to solving simultaneous linear equations. Start by drawing a line through two points. Create a second line which goes through the intersecting point. Background knowledge of how to find the equation of a line and...
EngageNY
Equations for Lines Using Normal Segments
Describing a line using an algebraic equation is an essential skill in mathematics. The previous lesson in the series challenged learners to determine if segments are perpendicular with a formula. Now they use the formula to determine...
Curated OER
Parallel and Perpendicular Lines
Fourth graders create a dance with a partner that shows parallel and perpendicular lines. In this lines lesson plan, 4th graders create symmetrical designs and line pairs with their partner.
Curated OER
Parallelism in Our Everyday World: Parallel Lines and Beyond
Students broaden their outlook on geometry in their everyday environment. They explore the properties of parallel lines and parallelograms and discover ways to prove the existence of parallel lines and discuss the concept of parallel lines.
Illustrative Mathematics
The Circle and The Line
Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...
Illustrative Mathematics
Proportional Relationships, Lines, and Linear Equations
The resource is a good introduction to what makes a proportional relationship between two lines. Discuss the similarities of both lines and the possibility of intersection. Use this opportunity to list other acceptable forms of each...
Curated OER
Parallel and Perpendicular Lines
Learners study parallel and perpendicular lines. For this parallel and perpendicular lesson, pupils explore 2-D shapes and determine if the sides are parallel or perpendicular.
Curated OER
Introduction to Parallel Lines in Euclidean Space and in Spherical Space
Eighth graders are introduced to the basic concepts of Geometry and their definitions in Euclidean space. They draw and define the following terms: point, line, and line segment. Students also define the terms colliner and...
Curated OER
Lesson Plan One: Points, Lines, Rays
Fifth graders explore basic geometric terms. Pupils draw a physical picture of a scene that illustrates at least five geometric terms. Partners exchange drawings and locate the illustration of geometric terms in the drawing.
Curated OER
Math A Regents Questions: Points on a Line
In this linear equations worksheet, young scholars solve 3 multiple choice problems. Students determine if a given point lies on a line given an equation of that line.