*Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.*

### General Information

**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

**Assessed:**Yes

### Test Item Specifications

**Assessment Limits :**

Items may assess relationships between vertical angles, special angles

formed by parallel lines and transversals, angle bisectors, congruent

supplements, congruent complements, and a perpendicular bisector

of a line segment.Items may have multiple sets of lines and angles.

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 lines.Students will prove theorems about angles.

Students will use theorems about lines to solve problems.

Students will use theorems about angles 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.

### Sample Test Items (2)

**Test Item #:**Sample Item 1**Question:**In the figure, . Let measure (3x+4)º, measure(6x-8)º, and measure (7x-20)º.

Click on the blank to enter the degree measure that completes the equation shown.

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**Complete the proof by dragging the correct reasons to the table for line 3 and 6.

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

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Educational Game

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Problem-Solving Tasks

## Tutorials

## MFAS Formative Assessments

Students are asked to prove that a point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment.

Students are asked to find the measures of angles formed by three concurrent lines and to justify their answers.

Students are asked to find the measures of angles formed by two parallel lines and a transversal.

Students are asked to find the measures of angles formed by two parallel lines and two transversals.

Students are asked to describe a triangle whose vertices are the endpoints of a segment and a point on the perpendicular bisector of a segment.

In a diagram involving two parallel lines and a transversal, students are asked to use rigid motion to prove that alternate interior angles are congruent.

Students are asked to identify a pair of vertical angles in a diagram and then prove that they are congruent.

## Student Resources

## Educational Game

Play a game to discover the relationship between opposite angles and identify names of angles by their measures. Students may select **Teach Me** to learn about these angle relationships prior to beginning play. Hints and feedback are provided to players.

Type: Educational Game

## Problem-Solving Tasks

This task asks students to show how certain points on a plane are equidistant to points on a segment when placed on a perpendicular bisector.

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

## Tutorials

In this tutorial, students will find the measures of angles formed when a transversal cuts two parallel lines.

Type: Tutorial

This tutorial shows students the eight angles formed when two parallel lines are cut by a transversal line. There is also a review of triangles in this video.

Type: Tutorial

Students will see in this tutorial the eight angles formed when two parallel lines are cut by a transversal line.

Type: Tutorial

In this tutorial, students will learn the angle measures when two parallel lines are cut by a transversal line.

Type: Tutorial

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

In this tutorial, students prove that vertical angles are equal. Students should have an understanding of supplementary angles before viewing this video.

Type: Tutorial

Students will use algebra to find the measure of vertical angles, or angles opposite each other when two lines cross. Students should have an understanding of complementary and supplementary angles before viewing this video.

Type: Tutorial

In this tutorial, students will use their knowledge of supplementary, adjacent, and vertical angles to solve problems involving the intersection of two lines.

Type: Tutorial

We will use algebra in order to find the measure of angles formed by a transversal.

Type: Tutorial

We will be able to identify corresponding angles of parallel lines.

Type: Tutorial

We will gain an understanding of how angles formed by transversals compare to each other.

Type: Tutorial

This 5 minute video gives the proof that vertical angles are equal.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

This task asks students to show how certain points on a plane are equidistant to points on a segment when placed on a perpendicular bisector.

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