*Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.*

**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Congruence

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

**Cluster:**Prove geometric theorems. (Geometry - Major 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 assess theorems and their converses for interior triangle

sum, base angles of isosceles triangles, mid-segment of a triangle,

concurrency of medians, concurrency of angle bisectors, concurrency

of perpendicular bisectors, triangle inequality, and the Hinge

Theorem.Items may include narrative proofs, flow-chart proofs, two-column

proofs, or informal proofs.In items that require the student to justify, the student should not be

required to recall from memory the formal name of a theorem.**Calculator :**Neutral

**Clarification :**

Students will prove theorems about triangles.Students will use theorems about triangles to solve problems

**Stimulus Attributes :**

Items may be set in a real-world or mathematical context**Response Attributes :**

Items may require the student to give statements and/or

justifications to complete formal and informal proofs.Items may require the student to justify a conclusion from a

construction.

**Test Item #:**Sample Item 1**Question:**Drag statements from the statements column and reasons from the reasons column to their correct location to complete the proof.

**Difficulty:**N/A**Type:**DDHT: Drag-and-Drop Hot Text

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## Tutorials

## MFAS Formative Assessments

Students are asked to explain why the sum of the lengths of the diagonals of an isosceles trapezoid is less than its perimeter.

Students are asked to explain why the sum of the measures of the interior angles of a convex *n*-gon is given by the formula (*n* – 2)180°.

Students are asked to prove that the base angles of an isosceles triangle are congruent.

Students are given a triangle in which the midpoints of two sides are shown and are asked to describe a method for locating the midpoint of the remaining side using only a straight edge and pencil.

Students are asked to prove that the medians of a triangle are concurrent.

Students are asked to prove the Triangle Inequality Theorem.

Students are given the measure of one interior angle of an isosceles triangle and are asked to find the measure of another interior angle.

Students are given the lengths of two sides of a triangle and asked to describe all possible lengths of the remaining side.

Students are asked to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side of the triangle and half of its length.

Students are asked prove that the measures of the interior angles of a triangle sum to 180°.

Students are asked to explain why a quadrilateral formed by drawing the midsegments of a triangle is a parallelogram and to find the perimeter of the triangle formed by the midsegments.

## Student Resources

## Problem-Solving Tasks

This problem solving task asks students to find the area of an equilateral triangle.

Type: Problem-Solving Task

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

Type: Problem-Solving Task

## Tutorials

In this video, students will learn how to use what they know about the sum of angles in a triangle to determine the sum of the exterior angles of an irregular pentagon.

Type: Tutorial

Lets prove that the sum of interior angles of a triangle are equal to 180 degrees.

Type: Tutorial

Let's find the measure of an angle, using interior and exterior angle measurements.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

This problem solving task asks students to find the area of an equilateral triangle.

Type: Problem-Solving Task

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

Type: Problem-Solving Task