10-H Geometry: Key Theorems, Properties, Definitions, Parallel Lines, Congruent Triangles, and Quadrilaterals

base

One of the 2 parallel sides of a trapezoid

base angles

Angles formed by the base and one of the legs of a trapezoid.

diagonal

A straight line connecting any two vertices of a polygon that are not adjacent

isosceles trapezoid

a trapezoid whose nonparallel opposite sides are congruent

legs

the nonparallel sides of a trapezoid

midsegment (median) of a trapezoid

a segment that connects the midpoints of the legs of a trapezoid. Length= avg. of bases

Parallelogram

a quadrilateral with both pairs of opposite sides parallel

rectangle

A parallelogram with four right angles

Rhombus

A parallelogram with four congruent sides

square

A parallelogram with four congruent sides and four right angles.

Trapezoid

A quadrilateral with exactly one pair of parallel sides

kite

a quadrilateral with exactly two pairs of congruent consecutive sides; 1 pair of opposite angles congruent

Polygon Angle Sum Theorem

The sum of the measures of the angles of a convex n-gon is (n-2)180

Polygon Exterior Angle Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

A triangle with 3 acute angles

acute triangle

The two angles opposite the congruent sides of an isosceles triangle

base angles

changes the position of the figure without changing its size or shape

congruence transformation

triangles that have all corresponding parts (sides & angles) congruent

congruent triangles

matching parts of congruent polygons

corresponding parts

all angles are congruent

equiangular

all sides are congruent

equilateral

an angle formed by one side of a triangle and the extension of another side

exterior angle

the angle between two sides of a triangle

included angle (of a triangle)

The side of a triangle that is between two given angles.

included side (of a triangle)

a triangle with at least two congruent sides

isosceles triangle

a triangle with one obtuse angle

obtuse triangle

A transformation that "flips" a figure over a reflection line; "mirror image"

Reflection

an interior angle that is not adjacent to the exterior angle

remote interior angles

a triangle with one right angle

right triangle

a triangle with no congruent sides

scalene triangle

The angle formed by the legs of an isosceles triangle.

vertex angle

The sum of the measures of the angles of a triangle is 180.

Angle Sum Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Exterior Angle Theorem

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

isoscles triangle theorem

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

Converse of the Isosceles Triangle Theorem

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SSS Postulate

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.

SAS

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

ASA

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

AAS Theorem

corresponding parts of congruent triangles are congruent

CPCTC

Parallel Lines

Lines on a plane that never meet. They are always the same distance apart.

Perpendicular Line

Lines that are at right angles (90°) to each other.

Perpendicular Bisector

A line which cuts a line segment into two congruent parts at 90°.

Transversal

A line that intersects at least two other lines in different points.

Alternate Interior Angles

angles between 2 lines and on opposite sides of a transversal

Alternate Exterior Angles

Angles that lie outside a pair of lines and on opposite sides of a transversal.

Consecutive/Same-Side Interior Angles

two angles that lie between the two lines and on the same side of the transversal

Corresponding Angles

Angles in the same place on different lines

Law of Detachment

If the hypothesis of a true conditional is true, then the conclusion is true.

Law of Syllogism

If p->q is true and q->r is true, then p->r is true.

Symmetric Property

If AB = CD then CD = AB and If

Transitive Property

If AB = CD and CD = EF then AB = EF. If

Reflexive Property

AB = AB and

Vertical Angles Theorem

Vertical Angles are congruent.

Congruent Supplements Theorem

If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.

Congruent Complements Theorem

If two angles are complements of the same angle (or congruent angles), then the two angles are congruent.

Definition of Midpoint

A midpoint of a segment is the point that divides the segment into two congruent segments.

Definition of Right Angle

A right angle is an angle whose measure if 90.

Definition of Congruent Angles

Congruent angles are angles that have the same measure.

Definition of Segment Bisector

A segment bisector is a line segment ray or plane that intersects a segment at its midpoint.

Definition of Angle Bisector

An angle bisector is a ray that divides an angle into two congruent angles.

Definition of Congruent Segments

Congruent segments are segments that have the same length.

Definition of Complementary Angles

Two angles are complementary if the sum of their measures is 90.

Definition of Supplementary Angles

Two angles are supplementary if the sum of their measures is 180.

Definition of Isosceles Triangle

An isosceles triangle has at least two congruent sides.