Geometry: Angle Relationships and Triangle Inequality

Vocabulary flashcards reviewing angle definitions, angle pair properties, and the triangle inequality theorem based on classroom lecture notes.

Supplementary Angles

A pair of angles whose measures add up to $180^\circ$ (such as angles AGD and FGC). They cannot both be acute, and they do not necessarily require one angle to be obtuse if both are right angles.

Complementary Angles

A pair of angles whose measures sum to $90^\circ$ (such as angles FGE and GBC). Two complementary angles can both be acute, and they do not have to be adjacent.

Vertical Angles

A pair of opposite angles formed by intersecting lines (such as angles GBC and FGE). They are sometimes complementary, but not always complementary.

Obtuse Angle

An angle with a measure strictly between $90^\circ$ and $180^\circ$, such as angle FGD.

Acute Angle

An angle whose measure is strictly less than $90^\circ$, such as angle BGC.

Supplement of an Acute Angle

An angle that pairs with an acute angle to total $180^\circ$, which is always an obtuse angle rather than another acute angle.

Complement of an Acute Angle

An angle that pairs with an acute angle to total $90^\circ$, which is always another acute angle.

Triangle Inequality Theorem

The geometric rule stating that the sum of the lengths of any two sides of a triangle must be strictly greater than the remaining side length (for example, sides $9$, $7$, and $14$ form a triangle because $9 + 7 = 16 > 14$, whereas $5$, $12$, and $18$ do not because $5 + 12 = 17 < 18$).