ACP Geometry Unit 2 Review

Vocabulary flashcards covering geometry postulates, angle pair relationships, parallel line theorems and converses, and linear equation forms from Unit 2.

Postulate on Two Points (Section 2.4)

Through any $2$ points, there is exactly one line.

Postulate on Three Noncollinear Points (Section 2.4)

Through any $3$ noncollinear points, there is exactly one plane.

Line Content Postulate (Section 2.4)

A line contains at least $2$ points.

Plane Content Postulate (Section 2.4)

A plane contains at least $3$ noncollinear points.

Intersection of Two Lines Postulate (Section 2.4)

If two lines intersect, then their intersection is exactly one point.

Intersection of Two Planes Postulate (Section 2.4)

If two planes intersect, then their intersection is a line.

Linear Pair

A pair of adjacent angles whose noncommon sides are opposite rays; their angle measures sum to $180^\beta$.

Vertical Angles (Vertical Pair)

Two nonadjacent angles formed by two intersecting lines; they are congruent ($\angle 1 \cong \angle 2$).

Angle Addition Postulate

A postulate stating that if a point $F$ lies in the interior of $\angle BCD$, then $m\angle BCF + m\angle FCD = m\angle BCD$.

Complementary Angles

Two angles whose measures have a sum of $90^\beta$.

Transversal

A line (such as line $p$) that intersects two or more coplanar lines at different points.

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, each pair of consecutive interior angles is supplementary (their measures sum to $180^\beta$).

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, each pair of alternate interior angles is congruent.

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, each pair of alternate exterior angles is congruent.

Corresponding Angles Theorem / Postulate

If two parallel lines are cut by a transversal, each pair of corresponding angles is congruent.

Consecutive Interior Angles Converse

If two lines are cut by a transversal so that consecutive interior angles are supplementary ($m\angle 1 + m\angle 2 = 180^\beta$), then the lines are parallel.

Alternate Interior Angles Converse

If two lines are cut by a transversal so that alternate interior angles are congruent ($\angle 1 \cong \angle 2$), then the lines are parallel.

Alternate Exterior Angles Converse

If two lines are cut by a transversal so that alternate exterior angles are congruent ($\angle 1 \cong \angle 2$), then the lines are parallel.

Point-Slope Form

The linear equation form given by $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a given point on the line.

Slope-Intercept Form

The linear equation form given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Slopes of Parallel Lines

Two nonvertical lines are parallel if and only if their slopes are equal ($m_1 = m_2$).

Slopes of Perpendicular Lines

Two nonvertical lines are perpendicular if and only if their slopes are opposite (negative) reciprocals ($m_1 \cdot m_2 = -1$).