Cluster 1: Understand and apply theorems about circles. (Geometry - Additional Cluster)Archived

You are a robotic spider tangled up in an angular web. Use your knowledge of angle relationships to collect flies and teleport through wormholes to rescue your spider family!

Type: Educational Game

Students are asked to describe the relationship between a central angle and an inscribed angle that intercept the same arc.

Type: Formative Assessment

Students are asked to construct a tangent line to a given circle from a given exterior point.

Type: Formative Assessment

Students are asked to draw a circle, a tangent to the circle, and a radius to the point of tangency. Students are then asked to describe the relationship between the radius and the tangent line.

Type: Formative Assessment

Students are asked to prove that opposite angles of a quadrilateral, inscribed in a circle, are supplementary.

Type: Formative Assessment

Students are asked to find the measures of two inscribed angles of a circle.

Type: Formative Assessment

Students are asked to complete and justify the construction of a line tangent to a circle from an exterior point.

Type: Formative Assessment

Students are given two circles with different radii and are asked to prove that the circles are similar.

Type: Formative Assessment

Students are given a diagram with inscribed, central, and circumscribed angles and are asked to identify each type of angle, determine angle measures, and describe relationships among them.

Type: Formative Assessment

Students are given two circles with different radius lengths and are asked to prove that the circles are similar.

Type: Formative Assessment

Students are asked to use a compass and straightedge to construct an inscribed circle of an acute scalene triangle.

Type: Formative Assessment

Students are asked to use a compass and straightedge to construct a circumscribed circle of an acute scalene triangle.

Type: Formative Assessment

Type: Lesson Plan

Students will apply concepts related to circles, angles, area, and circumference to a design situation.

Type: Lesson Plan

This lesson allows students to prove that all circles are similar using transformations. Students will need prior knowledge of similarity, transformations, and the definition of a circle. The lesson begins with a warm up regarding dilations, then poses the question: Are all circles similar? The students are guided through the proof using a translation and dilation. The teacher emphasizes the details in the proof. The lesson closes with an exit ticket.

Type: Lesson Plan

Students use coordinate based translations and dilations to prove circles are similar.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties:

• Solving problems by determining the lengths of the sides in right triangles.
• Finding the measurements of shapes by decomposing complex shapes into simpler ones.

The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties solving problems by determining the lengths of the sides in right triangles and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Type: Lesson Plan

Students learn and apply vocabulary, notation, concepts, and geometric construction techniques associated with circles and their tangents to a historical real-world scenario, the Mason-Dixon Line, and a hypothetical real-world scenario, the North-South Florida Line.

Type: Lesson Plan

This lesson is designed to enable students to develop strategies for describing relationships between right triangles and the radii of their inscribed and circumscribed circles.

Type: Lesson Plan

Students will start this lesson with a win-lose-draw game to review circle vocabulary words. They will then use examples on a discovery sheet to discover the relationships between arcs and the angles whose vertex is located on a circle, in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and questions answered on white boards.

Type: Lesson Plan

Students will start this lesson with a "Pictionary" game to review circle vocabulary terms. They will then use computers and GeoGebra to discover the relationships between portions of segments that intersect in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and consensus on rules (formulas).

Type: Lesson Plan

Discover how easy it is for Katie to construct an inscribed circular logo on her company's triangular pennant template. If she completes the task first, she will win a $1000 bonus! Follow along with this interactive tutorial.

Type: Original Student Tutorial

Learn the steps to circumscribe a circle around a triangle in this interactive tutorial about constructions. Grab a compass, straightedge, pencil and paper to follow along!

Type: Original Student Tutorial

What better way to demonstrate that all circles are similar then to use pizzas! Gaines Street Pies explains how all pizza pies are similar through transformations.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Type: Problem-Solving Task

This problem solving task challenges students to describe and compare different angles.

Type: Problem-Solving Task

This problem solving task asks students to explain certain characteristics about a triangle.

Type: Problem-Solving Task

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem.

Type: Problem-Solving Task

This problem solving task asks students to place a fire hydrant so that it is equal distance from three given points.

Type: Problem-Solving Task

This problem solving task challenges students to place a warehouse (point) an equal distance from three roads (lines).

Type: Problem-Solving Task

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle.

Type: Problem-Solving Task

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment.

Type: Problem-Solving Task

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Type: Problem-Solving Task

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Type: Problem-Solving Task

This problem solving task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

Type: Problem-Solving Task

This GeoGebraTube interactive worksheet shows you the step by step method for constructing tangent lines to a circle from a point outside the circle.  Use the slider to see each step, and read below the illustration to follow the steps.  

Type: Tutorial

In this GeoGebraTube interactive worksheet, you can watch the step by step process of circumscribing a circle about a triangle.  Using paper and pencil along with this resource will reinforce the concept.

Type: Virtual Manipulative

This problem solving task shows how to inscribe a circle in a triangle using angle bisectors.

Type: Worksheet