Students learn about common geometry tools and then learn to use protractors (and Miras, if available) to create and measure angles and reflections. The lesson begins with a recap of the history and modern-day use of protractors, compasses and mirrors. After seeing some class practice problems and completing a set of worksheet-prompted problems, students share their methods and work. Through the lesson, students gain an awareness of the pervasive use of angles, and these tools, for design purposes related to engineering and everyday uses. This lesson prepares students to conduct the associated activity in which they “solve the holes” for hole-in-one multiple-banked angle solutions, make their own one-hole mini-golf courses with their own geometry-based problems and solutions, and then compare their “on paper” solutions to real-world results.

Download these worksheets to sharpen your geometry skills. Sheets focus on angles, coordinate geometry, triangles, quadrilaterals, transformations, and three-dimensional geometry, and more.

This 20-day module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in their work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation. Through decomposition and composition activities as well as an exploration of symmetry, students recognize specific attributes present in two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures based on them.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

This is an introductory lesson about the trigonometric function sine. Students will study several similar right triangles and the ratio of certain two sides in them.

This fourth-grade geometry lesson teaches the definitions for a line, ray, angle, acute angle, right angle, and obtuse angle. We also study how the size of the angle is ONLY determined by how much it has "opened" as compared to the whole circle. The lesson contains many varied exercises for students.

At the end of this lesson, students will be able to identify and apply the properties of lines and angles and understand the concept of parallel, perpendicular, complementary and supplementary angles, vertical angles, and parallel lines cut by a transversal.

In this lesson, students will form cubes and discuss their attributes including edges, faces, vertices, and angles. Media resources and teacher materials are included.

In this lesson, students will create cubes and identify the attributes of a cube, including discussion of edges, faces, vertices, and angles. Teacher resources are provided.

In this lesson, students observe symmetry, geometric shapes, and angles in two Early American dances, and then choreograph their own dance with symmetrical figures. Media and teaching materials are included.

In this lesson, students use line segments, angles, and parallel and perpendicular lines in order to create a one point perspective drawing.

This video [4:39] provides an opportunity to learn about the characteristics of polygons. As you watch and listen to the teacher and student interact it helps clarify the thinking behind applying this concept.

Constructions and Angles

Unit Overview

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Use a protractor and ruler.
Identify different types of triangles and quadrilaterals and their characteristics.

Lesson Flow

After an initial exploratory lesson involving a paper folding activity that gets students thinking in general about angles and figures in a context, the unit is divided into two concept development sections. The first section focuses on types of angles—adjacent, supplementary, complementary, and vertical—and how they are manifested in quadrilaterals. The second section looks at triangles and their properties, including the angle sum, and how this affects other figures.

In the first set of conceptual lessons, students explore different types of angles and where the types of angles appear in quadrilaterals. Students fold paper and observe the angles formed, draw given angles, and explore interactive sketches that test many cases. Students use a protractor and ruler to draw parallelograms with given properties. They explore sketches of parallelograms with specific properties, such as perpendicular diagonals. After concluding the investigation of the angle types, students move on to the next set.

In the second set of conceptual development lessons, students focus on triangles. Students again fold paper to create figures and certain angles, such as complementary angles.

Students draw, using a protractor and ruler, other triangles with given properties. Students then explore triangles with certain known and unknown elements, such as the number of given sides and angles. This process starts with paper folding and drawing and continues with exploration of interactive sketches. Students draw conclusions about which cases allow 0, 1, 2, or an infinite number of triangles. In the course of the exploration, students discover that the sum of the measure of the interior angles of a triangle is 180°. They also learn that the sum of the measures of the interior angles of a quadrilateral is 360°. They explore other polygons to find their angle sum and determine if there is a relationship to angle sum of triangles. The exploration concludes with finding the measure of the interior angles of regular polygons and speculating about how this relates to a circle.

Lastly, students solve equations to find unknown angle measures. Using their previous experience, students find the remaining angle measures in a parallelogram when only one angle measure is given. Students also play a game similar to 20 Questions to identify types of triangles and quadrilaterals. Having completed the remaining lessons, students have a four-day Gallery to explore a variety of problems.

The unit ends with a unit assessment.

Students learn more about the characteristics of parallelograms by folding paper and measuring the angles in a parallelogram. Students use a ruler and protractor to draw parallelograms with given properties. Then, students use a ruler and protractor to draw a rectangle.Key ConceptsOpposite angles of a parallelogram are congruent.Consecutive angles of a parallelogram are supplementary.Diagonals of a parallelogram bisect each other.Diagonals of a rectangle are congruent.Goals and Learning ObjectivesAccess prior knowledge of parallelograms.Understand that the sum of angle measures in any quadrilateral is 360°.Understand the relationship of the angles and diagonals in a parallelogram.Understand the relationship of the angles and diagonals in a rectangle.

Students learn how the diagonals of a rhombus are related. They use interactive sketches to learn about the properties of the angles and diagonals of squares, rectangles, rhombuses, parallelograms, and other quadrilaterals.Key ConceptsThe sum of the measures of the angles of all quadrilaterals is 360°.The alternate angles (nonadjacent angles) of rhombuses and parallelograms have the same measure.The measure of the angles of rectangles and squares is 90°.The consecutive angles of parallelograms and rhombuses are supplementary. This applies to squares and rectangles as well.The diagonals of a parallelogram bisect each other.The diagonals of a rectangle are congruent and bisect each other.The diagonals of a rhombus bisect each other and are perpendicular.Goals and Learning ObjectivesMeasure the angles formed by the intersection of the diagonals of a rhombus.Explore the relationships of the angles of different squares, rectangles, rhombuses, parallelograms, and other quadrilaterals.Explore the relationships of the diagonals of different squares, rectangles, rhombuses, parallelograms, and other quadrilaterals.

Students learn about four types of angles: adjacent, vertical, supplementary, and complementary. They explore the relationships between these types of angles by folding paper, measuring angles with a protractor, and exploring interactive sketches.Key ConceptsAdjacent angles are two angles that share a common vertex and a common side, but do not overlap. Angles 1 and 2 are adjacent angles.Supplementary angles are two angles whose measures have a sum of 180°. Angles 3 and 4 are supplementary angles. Complementary angles are two angles whose measures have a sum of 90°. Angles 5 and 6 are complementary angles. Vertical angles are the opposite angles formed by the intersection of two lines. Vertical angles are congruent. Angles 1 and 2 are vertical angles. Angles 3 and 4 are also vertical angles.Goals and Learning ObjectivesMeasure angles with a protractor and estimate angle measures as greater than or less than 90°.Understand the definition of vertical, adjacent, supplementary, and complementary angles.Explore the relationships between these types of angles.

This multimedia Learn Alberta math resource focuses on the many triangles that are found in our everyday environment. The accompanying interactive component asks students to find triangles in a picture and to solve for the missing angles in the diagram. Be sure to follow the link to the printable activity included to reinforce target skills. The resource begins with a short video [1:22] and is followed by more interactive activities.

Everything you wanted to know about angles and more, including 1) how to measure angles 2) types of angles 3) angle relationships and 4) angles around a transversal.

A complete reference guide to circles including parts, angles, and arcs. It provides definitions and interactive activities that enhance further explanation.