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)

- demonstrate how a straight line segment can be drawn joining any two points (Euclid’s first
- 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.

- given any two objects (non-geometric), describe what is the same and different about them
**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).

- 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).

- use the compass points to justify that all radii are equidistant and congruent
**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

- justify that two segments take up the same
**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

- explain that the
- 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.*

- given a line segment, create a congruent segment, and explain why they are congruent

Develop conceptual understanding:

congruent, incongruent, point, line, ray, line segment, postulate, length measure, circle, radius, equidistant, distance, bisect, midpoint, segment additionSupporting terms to communicate:

compass, straightedge, construction, collinear, coplanar, plane, space, partition, centerpoint, arc, coordinate grid