**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Circles

**Cluster:**Level 3: Strategic Thinking & Complex Reasoning

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

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Items may include problems that use the incenter and circumcenter

of a triangle.**Calculator :**Neutral

**Clarification :**

Students will construct a circle inscribed inside a triangle.Students will construct a circle circumscribed about a triangle.

Students will solve problems using the properties of inscribed and

circumscribed circles of a triangle.Students will use or justify properties of angles of a quadrilateral that

is inscribed in a circle.**Stimulus Attributes :**

Item may be set in real-world or mathematical context.**Response Attributes :**

Items may require the student to use or choose the correct unit of

measure.Items may require the student to provide steps for a construction.

Items may require the student to give statements and/or

justifications to complete formal and informal proofs.

**Test Item #:**Sample Item 1**Question:**Trapezoid ABCD is inscribed in circle O. Diagonals meet at point E and is parallel to , as shown.

Select the angles and value that make a true statement about trapezoid ABCD.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Virtual Manipulative

## Worksheet

## MFAS Formative Assessments

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

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

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

## Original Student Tutorials Mathematics - Grades 9-12

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!

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.

## Student Resources

## Original Student Tutorials

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

## Problem-Solving Tasks

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 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

## Virtual Manipulative

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

## Worksheet

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

Type: Worksheet

## Parent Resources

## Problem-Solving Tasks

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 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

## Worksheet

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

Type: Worksheet