Definitions Assessment Bank Document
HSG-CO.A.1 High School Geometry Assessment
Definitions Assessment Bank Document
Testing Precise Definitions & Undefined Notions in Geometry
Name:
Date: Period:
A
Part 1: Undefined Notions & Core Concepts
1. Which geometric entity is considered an undefined term in Euclidean geometry?
A. Circle
B. Line
C. Line Segment
D. Perpendicular Line
2. Which of the following provides the mathematically precise definition of a circle?
A. A curved geometric shape that has no corners and encloses 360 degrees.
B. The set of all points in a plane equidistant from a fixed center point.
C. A continuous round polygon with an infinite number of microscopic straight sides.
D. The path traced by a segment that turns around one endpoint indefinitely.
3. How is the size of an angle formally measured in axiomatic geometry?
A. By the straight-line distance between ray endpoints
B. By the length of the rays that make up the sides
C. By the distance around a circular arc centered at the vertex
D. By the total area enclosed between the two rays
B
Part 2: Formal Definition Construction
4. Define a line segment in terms of undefined notions (point, line, betweenness):
A line segment \(\overline{AB}\) is the set consisting of two distinct points \(A\) and \(B\) (called the ) and all points on line \(\overleftrightarrow{AB}\) that lie them.
5. Define perpendicular lines using intersecting lines and angles:
Two intersecting lines are perpendicular if and only if they meet to form four congruent , each having a measure of degrees.
6. Define parallel lines using coplanar lines and intersection:
Two lines in the same plane are parallel if and only if they , maintaining a constant distance between them.
Standard HSG-CO.A.1 • Question Bank & Assessment Page 1 of 2
Definitions Assessment Bank Document
Part 3: Critique & Analysis • Part 4: Extended Geometric Reasoning
Student Name:
C
Part 3: Critique & Error Analysis
7. Critique an Incomplete Parallel Lines Definition:
A student writes: "Parallel lines are two lines that never intersect."
Explain why this definition is incomplete in three-dimensional space, and rewrite it using the correct geometric qualification:
