GEOMETRY UNIT 4-TRIANGLES TERMS

Triangle Parts Relationship Theorem

The side opposite from the smallest angle will be the smallest side.

alternate exterior angles

Angles that lay outside the parallel lines and are on opposite sides of the transversal; They are congruent.

congruent

Having the same size and shape

angle bisector

a ray that divides an angle into two congruent angles

Base angle of an isosceles triangle

in an isosceles triangle, either of the two congruent angles along the base

converse

the statement formed by exchanging the hypothesis and conclusion of a conditional statement

linear pair

A pair of adjacent angles whose noncommon sides are opposite rays, so the angles are sum up to 180 degrees

perpendicular bisector

A line that is perpendicular to a segment at its midpoint.

inequality

A mathematical sentence that contains less than, greater than, less than or equal to, greater than or equal to, or not equal

acute triangle

A triangle with 3 acute angles

equiangular triangle

A triangle with 3 congruent angles

equilateral triangle

A triangle with three congruent sides

obtuse angle

An angle between 90 and 180 degrees

included angle

An angle created by two adjacent sides

Third Angle Theorem

If two angles in one triangle are congruent to two angles in another triangle then the third angle is also congruent.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite of those sides are congruent.

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.

same side exterior angles

Pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on the same side of the transversal and are outside the other two lines. When the two other lines are parallel, same-side exterior angles are supplementary.

vertex angle

The angle formed by the legs of an isosceles triangle.

Vertex Angle of an Isosceles Triangle Theorem

The bisector of a vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measure of the remote angles.

Interior Angle Sum Theorem

The sum of the three interior angles always add up to 180 degrees.

same side interior angles

The two angles that are inside (interior) the parallel lines and are on the same side of the transversal Are SUPPLEMENTARY (add up to 180 degrees)

isosceles triangle

a triangle with at least two congruent sides

scalene triangle

a triangle with no congruent sides

obtuse triangle

a triangle with one obtuse angle

right triangle

a triangle with one right angle

exterior angles

an angle formed by a side and an extension of an adjacent side

right angle

an angle that measures 90 degrees

acute angle

an angle that measures less than 90 degrees

alternate interior angles

angles between 2 lines and on opposite sides of a transversal

interior angles

angles formed by each pair of adjacent sides on the inside of a polygon

remote interior angles

the angles of a triangle that are not adjacent to a given exterior angle

corresponding angles

the angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are congruent

included side

the side between two angles

assume

to accept as true without proof

supplementary angles

two angles whose measures have a sum of 180 degrees