Back to Exercise: Define geometric terms precisely

Exercises: Precise Definitions of Geometric Terms

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Grade 9·20 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-co-a-1

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Recall / Warm-Up

These problems review geometry concepts from middle school.

In Euclidean geometry, which of the following is an undefined term — a starting point accepted without a formal definition?

Line segment

Angle

Point

Circle

Which geometric figure is formed by two rays that share a common endpoint?

A line segment

An angle

A circle

A line

Which best describes the difference between a defined term and an undefined term in geometry?

Defined terms are used in proofs; undefined terms are not.

Undefined terms are accepted as intuitive starting points; defined terms are built from those starting points.

Undefined terms are vague and imprecise; defined terms are exact.

Defined terms are invented by mathematicians; undefined terms come from nature.

Fluency Practice

Apply the precise definitions of each term.

$A straight line with arrows at both ends and two marked points, with the portion between the points emphasized.$

Which definition correctly describes a line segment?

The set of all points in a plane equidistant from a given center point

Two rays sharing a common endpoint

Part of a line consisting of two endpoints and all points between them

A straight path extending infinitely in both directions

An angle is formed by two ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ that share a common endpoint called the ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

lines … origin

line segments … midpoint

rays … vertex

lines … vertex

$Two perpendicular lines crossing at a point, with right-angle boxes marking all four 90-degree angles.$

Two lines are perpendicular if they intersect to form angles of what measure?

$45^\circ$

$90^\circ$

$180^\circ$

Any equal angle measure

Which statement gives the most precise definition of parallel lines?

Lines that look like they will never meet

Lines in the same plane that do not intersect

Lines that are the same distance apart at one location

Lines that run in the same direction

A circle is precisely defined as the set of all points in a plane that are ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ from a given point called the ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

inside a fixed distance … origin

equidistant … center

equidistant … vertex

within the boundary … center

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