12 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### Congruent segments have equal measure.

1 week

Evidence of Understanding

• describe the qualities that make two line segments congruent or incongruent
• given any two objects (non-geometric), describe what is the same and different about them
• Example: a pen and a pencil
• identify and justify why two objects are the same or different
• distinguish “exactly the same” from “alike”
• discuss the difference between points, lines, rays, and line segments in terms of congruence
• demonstrate how a straight line segment can be drawn joining any two points (Euclid’s first postulate)
• demonstrate how any straight line segment can be extended indefinitely in a straight line (Euclid’s second postulate)
• justify which qualities are significant or insignificant for determining if two segments in geometry are congruent
• Example: length measure vs.color of the segment, thickness, etc.
• define radius as a relationship between a circle’s center and points on the circle
• use the compass points to justify that all radii are equidistant and congruent
• explain how given any straight lines segment, a circle can be drawn having the segment as radius and one endpoint as center (Euclid’s third postulate).

• construct congruent segments and justify their congruence
• given a line segment, create a congruent segment, and explain why they are congruent
• use notation to signify congruence
• describe how a compass can be used to construct congruent segments
• justify that two segments take up the same distance in space
• consider and describe implications of human error
• bisect a line segment and justify congruence of both parts
• explain that the midpoint bisects a line segment
• use segment addition to explain that each part is half the measure of the whole
• compare methods for determining congruence and describe advantages of each type
• Examples: paper folding, placing the segment (vertical and horizontal only) on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.

Develop conceptual understanding:

congruent, incongruent, point, line, ray, line segment, postulate, length measure, circle, radius, equidistant, distance, bisect, midpoint, segment addition

Supporting terms to communicate:

compass, straightedge, construction, collinear, coplanar, plane, space, partition, centerpoint, arc, coordinate grid
Core Resource
A core resource supports multiple days of instruction.
• Introduction to Constructions
This multiple-day resource introduces students to constructions with a compass and straightedge.
Resource:
Introduction to Constructions

The objective of this activity is to support students with becoming comfortable making precise circles and line segments using a compass and a straight-edge or a ruler.

All Resources From:
• Unit 1

#### Tools of Geometry

Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.

• Proof Using a Construction
Students will use parts of a construction to prove a triangle is equilateral.
Resource:
Proof Using a Construction

Students will use parts of a construction to prove a triangle is equilateral.

All Resources From:
• Unit 1