CK-12 Geometry Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Geometry Student Edition. The solution and assessment guides are available upon request.

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

This review lesson about basic shapes (polygons)contains varied hands-on exercises and tilings about triangles, quadrilaterals, pentagons, and hexagons.

Brush up on your math skills relating to the area of parallelograms then try some practice problems to test your understanding.

Brush up on your math skills relating to the area of rhombuses then try some practice problems to test your understanding.

Brush up on your math skills relating to the area of trapezoids then try some practice problems to test your understanding.

Brush up on your math skills relating to the types of quadrilaterals then try some practice problems to test your understanding.

Learn about the properties of rectangles, rhombuses, and squares, and practice identifying them. Includes hints for questions. CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories

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Quadrilaterals-parallelograms, rectangles, and trapezoids-are thoroughly introduced in this lesson plan for upper elementary and middle school students. Lots of resources are linked to it to help support the teacher and students. CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories

A detailed introduction to quadrilaterals, the different types, and the vocabulary used to discuss their properties and to classify them. [8:24]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Gain a basic understanding of quadrilaterals by watching this easy to understand video tutorial. Additional resources are available as part of a paid subscription service. [9:49]

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.

Lesson OverviewStudents explore different polygons by drawing them, measuring angles, and manipulating interactive sketches to find the angle sum for any polygon. Students also explore the angle measures in regular polygons.Key ConceptsThe angle sum in a triangle is 180°. A quadrilateral can be composed of two triangles, so the angle sum of a quadrilateral is 360°.The number of triangles that compose a polygon is two less than the number of sides (angles). The sum of the interior angles in a polygon with n sides is 180° (n – 2).Goals and Learning ObjectivesFind angle sums in polygons.Generalize to find the angle sum for any polygon.Find interior angle measures for regular polygons. 

Gallery OverviewAllow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit’s concepts or to assist students who may have fallen behind on work.Problem DescriptionsParallelogram to CubeStudents have a chance to review angle measurements in a parallelogram. Building the cube helps students see the transition from two-dimensional shapes and their relationship to three-dimensional figures.QuadrilateralsStudents investigate the possible quadrilaterals that can be made from any four given side lengths, focusing on those that can’t make a quadrilateral. Students also look at possible parallelograms with two sides given and possible rhombuses with four sides given.DiagonalsStudents further investigate diagonals in quadrilaterals. If the diagonals are perpendicular, is the figure a rhombus?TrapezoidsHow many right angles can a trapezoid have? How many congruent angles or congruent sides can it have? Can its diagonals be perpendicular or congruent? Students investigate possible trapezoids.More AnglesStudents explore three intersecting lines and the combinations of angles.Diagonals and AnglesThe sides of a parallelogram are extended beyond the vertices, and students explore which angles are congruent and which are supplementary. Students also explore the effect diagonals have on interior angles.Exterior AnglesStudents  explore the sum of exterior angles for several polygons and speculate about the results.Angles and SidesStudents explore the relationship between angles and sides in a triangle and discover that the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle (and congruent sides are opposite congruent angles).Ratios and AnglesStudents explore the ratios of the legs of a right triangle to the angles in the triangle. Students see that there is a unique ratio for each angle, and vice versa. This is an informal look at trigonometry.Find the AngleStudents solve equations to find angle measures in polygons.TessellationsStudents explore quadrilateral tessellations and why they tessellate. Students also explore tessellations of pentagons and other polygons.

Resize and rotate different types of quadrilaterals--square, rectangle, rhombus, trapezoid, and kite--while learning the definitions of these different shapes and labeling the angles and diagonals. CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories

This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

In this lesson on 2D shapes, students will learn to discriminate quadrilaterals from other polygons. Additionally, they will be able to identify attributes of a square, rectangle, and rhombus.

In this lesson on area and perimeter, students will learn how to find the area and perimeter of rectangles by applying formulas.