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Illustrative Mathematics

The Geometry of Letters

For Teachers 3rd - 5th Standards
Use the alphabet as a tool for teaching your class about geometric figures. Break apart capital letters into line segments and arcs. Classify angles as right, acute, or obtuse. Identify parallel and perpendicular lines. An excellent...
Lesson Plan
Curated OER

Triangle's Interior Angles

For Teachers 7th - 9th Standards
Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.
Lesson Plan
EngageNY

The Inscribed Angle Alternate – A Tangent Angle

For Teachers 9th - 12th Standards
You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their...
Lesson Plan
EngageNY

Secant Angle Theorem, Exterior Case

For Teachers 9th - 12th Standards
It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous lesson plan to investigate angles created by secant lines that intersect at a point exterior to the...
Interactive
CK-12 Foundation

Directed Line Segments: Dog Park

For Students 11th - Higher Ed Standards
Its a dog's world! Using a vector in standard position, pupils model the path a dog takes to different items in a dog park. The individuals use the interactive to find the magnitude and direction of the directed line segment.
Handout
El Paso Community College

Geometry Definitions

For Students 7th - 9th Standards
Geometry is full of shapes, figures, and corresponding things here and there. The guide shares all of the key pieces of geometric information in a nicely color-coded and labeled sheet. 
Lesson Plan
EngageNY

Solve for Unknown Angles—Angles and Lines at a Point

For Teachers 9th - 10th Standards
How do you solve for an unknown angle? In this sixth installment of a 36-part series, young mathematicians use concepts learned in middle school geometry to set up and solve linear equations to find angle measures.
Worksheet
Math Mammoth

Measuring Angles

For Students 4th - 6th Standards
The first of two pages displays various angles as the measure of degrees of a circular arc. An explanation is written, and learners are asked to model each by holding up two pencils as the rays. The second page provides instruction on...
Lesson Plan
West Contra Costa Unified School District

Arcs and Angles

For Teachers 9th - 12th
Noah didn't construct this kind of arc. High school scholars first explore how angles can be formed in circles. They then learn relationships between angles and arcs by conducting an exploratory activity where they position and draw arcs...
Interactive
CK-12 Foundation

Vertical Angles: Yo-Yo Eiffel Tower Trick

For Students 7th - 12th Standards
Yo, yo, learn about vertical angles with a yo-yo. Using an interactive, scholars adjust the position of fingers holding a design from a yo-yo. Answering a set of challenge questions based on the interactive helps clarify understanding of...
Interactive
CK-12 Foundation

Identify Line Types: Identify Types of Lines

For Students 6th - 12th Standards
If lines aren't parallel or perpendicular, then what are they? An interactive lets users rotate a line to change its orientation with respect to another line. It then indicates whether the lines are parallel, perpendicular, or...
Interactive
CK-12 Foundation

Parallel and Perpendicular Lines: Identify Types of Lines

For Students 9th - 11th
Are there only three options: parallel, perpendicular, or intersecting? Scholars move a given line in an interactive to change its orientation with respect to another line. The interactive indicates whether the lines are parallel,...
Interactive
CK-12 Foundation

Vectors as Directed Line Segments: Directed Line Segment

For Students 9th - 12th Standards
Direct your class' attention to directed line segments. The interactive resource allows pupils to create segments with specific endpoints. Scholars plot the initial and terminal points to determine the direction and magnitude of the...
Handout
McGraw Hill

Lines and Angles

For Students 4th - 7th Standards
Why was the obtuse angle upset? Because it was never right! A valuable resource is loaded with background information on types of angles and lines. Learners review the characteristics of parallel, perpendicular, and...
Lesson Plan
Virginia Department of Education

Lines and Angles

For Teachers 9th - 11th Standards
Explore angle relationships associated with transversals. Pupils construct parallel lines with a transversal and find the measures of the angles formed. They figure out how the different angles are related before constructing...
Worksheet
K12 Reader

Kinds of Angles

For Students 2nd - 3rd Standards
Have you ever wondered how circles and angles relate to each other? Read a passage about right angles, acute angles, and obtuse angles, and answer reading comprehension questions about the information you learn. 
Worksheet
Mt. San Antonio Collage

Postulates, Angles, and Their Relationships

For Students 8th - 11th Standards
More than a worksheet, learners go through geometry topics example by example on the nicely organized handout. From postulates to classifying angles, there are rules and examples provided for each topic. The ten pages of problems...
Worksheet
Lane Community College

Review Sheets: Geometry

For Students 8th - 11th
Full of problems with polygons, angles, lines, and triangles, your learners get a multi-page packet that provides all they need to know. It contains many of the standard problem types as well as some more challenging questions. 
Lesson Plan
EngageNY

Looking More Carefully at Parallel Lines

For Students 9th - 10th Standards
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...
Unit Plan
Mathematics Vision Project

Module 3: Geometric Figures

For Teachers 9th - 12th Standards
It's just not enough to know that something is true. Part of a MVP Geometry unit teaches young mathematicians how to write flow proofs and two-column proofs for conjectures involving lines, angles, and triangles.
Lesson Plan
EngageNY

Segments That Meet at Right Angles

For Teachers 9th - 12th Standards
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...
Lesson Plan
EngageNY

How Do Dilations Map Angles?

For Students 9th - 10th Standards
The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure. 
Lesson Plan
EngageNY

Secant Lines; Secant Lines That Meet Inside a Circle

For Teachers 9th - 12th Standards
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.
Interactive
CK-12 Foundation

Vertical Angles

For Students 7th - 10th Standards
Examine vertical angles from a different angle. Moving one line in an intersecting pair of lines lets users see relationships between vertical angles. They finish by answering some machine-scored questions on the topic.

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