Honors Geometry Unit 3 Review Flashcards

Vocabulary and theorem flashcards derived from the Honors Geometry Unit 3 Review notes, covering triangle congruence postulates, line relationships, angle theorems, and geometric proof terms.

Exterior Angle Theorem

A theorem stating that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Consecutive Interior Angles

Pairs of interior angles located on the same side of a transversal line intersecting two other lines. When the two lines are parallel, these consecutive interior angles (such as $\angle 1$ and $\angle 2$) are supplementary ($\angle 1 + \angle 2 = 180^\circ$).

Isosceles Triangle Theorem

A theorem stating that if two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Hypotenuse-Leg (HL) Theorem

A theorem stating that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the two triangles are congruent.

Angle Bisector

A ray, segment, or line that divides an angle into two congruent adjacent angles, such as segment $\overline{BD}$ bisecting $\angle ABC$ into $\angle 3 \cong \angle 4$.

Vertical Angles Theorem

A theorem stating that vertical angles—opposite angles formed by two intersecting straight lines—are congruent (for example, $\angle 1 \cong \angle 5$).

Transitive Property of Congruence

A property stating that if geometric figure $A$ is congruent to figure $B$, and figure $B$ is congruent to figure $C$, then figure $A$ is congruent to figure $C$.

Reflexive Property of Congruence

A property stating that any geometric figure is congruent to itself (for example, $\overline{BD} \cong \overline{BD}$ or $\overline{AC} \cong \overline{CA}$).

ASA Congruence Theorem

A theorem stating that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

CPCTC

An acronym standing for 'Corresponding Parts of Congruent Triangles are Congruent,' used in geometric proofs after establishing triangle congruence.

Alternate Interior Angles Converse Theorem

A theorem stating that if two lines are cut by a transversal and the alternate interior angles are congruent (such as $\angle 1 \cong \angle 4$), then the lines are parallel ($\overline{AD} \parallel \overline{BC}$).

Acute Scalene Triangle

A triangle with three acute interior angle measures (all less than $90^\circ$) and three unequal side lengths (e.g., a triangle with interior angles measuring $50^\circ$, $60^\circ$, and $70^\circ$).

Obtuse Scalene Triangle

A triangle that contains one angle measure greater than $90^\circ$ (obtuse) and three unequal side lengths (e.g., a triangle with angles measuring $35^\circ$, $40^\circ$, and $105^\circ$).

Perpendicular Bisector

A line, segment, or ray that intersects a line segment at its midpoint at a $90^\circ$ angle, dividing it into two equal congruent parts.

Triangle Angle Sum Theorem

A theorem stating that the sum of the interior angle measures of any triangle is always equal to $180^\circ$.

Slopes of Parallel Lines

Two distinct non-vertical lines in a plane are parallel if and only if they have equal slopes ($m_1 = m_2$).

Slopes of Perpendicular Lines

Two non-vertical lines in a plane are perpendicular if and only if their slopes are negative reciprocals of each other ($m_1 \cdot m_2 = -1$).

SAS Congruence Theorem

A theorem stating that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.