honors geometry unit one

Point

A location in space with no dimensions, represented by a dot.

Line

A straight one-dimensional figure that extends infinitely in both directions, defined by two points.

Plane

A flat two-dimensional surface that extends infinitely in all directions, defined by three non-collinear points.

Segment

A part of a line that consists of two endpoints and all points between them.

Ray

A part of a line that starts at one endpoint and extends infinitely in one direction.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie on the same plane.

Congruent Segments

Segments that have the same length.

Adjacent Angles

Two angles that share a common side and vertex but do not overlap.

Opposite Rays

Two rays that share an endpoint and extend in opposite directions.

Acute Angle

An angle whose measure is less than 90°.

Right Angle

An angle whose measure is exactly 90°.

Obtuse Angle

An angle whose measure is greater than 90° but less than 180°.

Angle Bisector

A ray that divides an angle into two congruent angles.

Complementary Angles

Two angles whose measures add up to 90°.

Intersection of Lines

The point where two lines meet.

Parallel Lines

Lines in the same plane that never intersect.

Intersection of Planes

The line where two planes meet.

Non-collinear Points

Points that do not all lie on the same line.

Reflection

A transformation that flips a figure over a line, creating a mirror image.

Translation

A transformation that slides a figure in a given direction without changing its shape or size.

Rotation

A transformation that turns a figure around a fixed point, known as the center of rotation.

90° Rotation Rule

(x, y) → (-y, x)

180° Rotation Rule

(x, y) → (-x, -y)

270° Rotation Rule

(x, y) → (y, -x)

Center of Rotation

The fixed point around which the figure rotates.

Reflect A(-3, 1) over x = -1

A’ = (-1, 1)

Translate P(1, 2) by

P’ = (-1, 6)

Rotate J(3, 0) 90° about origin

J’ = (0, 3)

Midpoint Theorem

The midpoint of a segment divides it into two congruent segments.

Segment Addition Postulate

If point B is between points A and C, then AB + BC = AC.

Angle Addition Postulate

If point D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC.

Vertical Angles

Angles opposite each other when two lines intersect; they are always congruent.

Linear Pair

A pair of adjacent angles formed when two lines intersect; they are supplementary (add up to 180°).

Complementary Angles

Two angles that add up to 90°.

Two segments are sometimes congruent.

True

Two points are always collinear.

True

The intersection of two planes is always a line.

True