Inscribed angles are central to the lesson. Young mathematicians build upon concepts learned in the previous lesson and formalize the Inscribed Angle Theorem relating inscribed and central angles. The lesson then guides learners to prove...

Right angles, acute angles, obtuse angles, central angles, inscribed angles: how many types of angles are there? Learners first investigate definitions of inscribed angles, central angles, and intercepted arcs. The majority of the...

How do you find the measure of an arc? Learners first review relationships between central and inscribed angles. They then investigate the relationship between these angles and their intercepted arcs to extend the Inscribed Angle Theorem...

We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson then...

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...

It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous lesson to investigate angles created by secant lines that intersect at a point exterior to the circle....

One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...

Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...

High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve...

Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.

All triangles have some things in common. Using these properties of triangles, learners find missing angle measures. Scholars use the Angle Sum Property and properties of special triangles throughout the instructional activity.

Students analyze inscribed angles and intercepted arcs and explore the relationships between the two. They investigate the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles.

What does it mean for a quadrilateral to be cyclic? Mathematicians first learn what it means for a quadrilateral to be cyclic. They then investigate angle measures and area in such a quadrilateral.

What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...

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...

Students differentiate between inscribed quadrilaterals and parallelograms. In this geometry activity, students identify the shaped of the polygons when it is inscribed inside of a circle. They calculate the missing angles of the...

Young scholars investigate basic geometric concepts. In this geometry lesson, students explore solids through measuring and modeling. This assignment models the importance of understanding concrete objects in geometry.      

Students discover how to recognize tangents and how to use their properties. They investigate and use the properties of angles, arcs, chords, tangents, and secants. Students use two tangents and the properties of similar triangles to...

Students use problem solving skills, formal geometry, and The Geometer?s Sketchpad. They model and solve two real-world problems by constructing the in center and circumcenter of triangles.

Seventh graders investigate the mathematical concept of a sector. They apply the concept to an example problem and then move into a more complex application. They find the area of the side of a cone. This is done as students calculate...

In this activity, students recognize the relationship of angles to circles. They study the Inscribed Angle Theorem and its corollaries.

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 with one side of the triangle a diameter. The fact that these...

This activity is designed to help students discover several important theorems concerning lengths of segments formed by intersecting chords, secants, and tangents.

The goal of this task is to help students synthesize their knowledge of triangles where only two of the vertices have been given. They will need to know that a triangle inscribed in a circle, with a diameter of the circle as one side, is...