Geometry Review and Vocab

Acute angle

An angle that measures less than 90 degrees

Acute triangle

A triangle whose angles all measure less than 90 degrees

Addition property of equality

If you add the same number to both sides of an equation, the two sides stay equal

Adjacent angles

Two angles that share a common vertex and one common side without overlapping

All of my children are bringing in peanut butter cookies

Altitude

Line segment from a vertex, perpendicular to the opposite side

Altitude rule

altitude/segment = hypotenuse/altitude

Altitude-hypotenuse theorem

In a right triangle, the altitude drawn to the hypotenuse creates two smaller right triangles similar to each other and to the original

Alternate interior angles

Angles formed on opposite sides of a transversal

Alternate interior angles theorem

When lines are parallel, alternate interior angles are congruent

Angle bisector

A ray that divides an angle into two congruent angles

Angle - angle similarity

If two angles of one triangle are congruent to two angles in another triangle, then the two triangles are similar

AAS Congruence

In two triangles, if two of their angles and their non-included side are congruent, then they are congruent

ASA Congruence

In two triangles, if two of their angles and their included side are congruent, then the triangles are congruent

Angles outside of circles

The external angle is half the measure of the large arc minus the measure of the smaller arc

Isosceles triangle apex rule

If two sides are equal, the two base angles are equal

Area

The amount of space inside a 2D shape, measured in square units

Area of a circle

A= Pi r² ( radius squared )

Area of a parallelogram

A=Bh

Area of a trapezoid

A=.5(B1 + B2)h

Area of a triangle

A = .5bh

Area of similar figures

A1/A2 = K squared, where k is the ratio of corresponding side lengths

Centroid

Point where a triangle's three medians intersect, "center of gravity”

Central angle

Angle whose vertex is at the center of the circle, is congruent to its intercepted arc

Chord

Line segment whose endpoints both lie on the circle

Circumcenter

Point where the perpendicular bisectors of a triangle's sides intersect, center of the circumscribed circle, equidistant from all vertices of the triangle

Colinear points

Points that lie on the same line

Common tangents

Lines that touch two circles at only one point

Complimentary angles

Two angles whose measures add up to 90 degrees

Composition

2 or more transformations in order, read right to left

Congruent chords theorem

If two chords are congruent, they are both equidistant from the center

Congruent complements theorem

If two angles are complements of the same or congruent angles, then those angles are congruent

Congruent supplements theorem

If two angles are supplements of the same or congruent angles, then those angles are congruent

Same side interior angles theorem

If lines are parallel, same side interior angles are supplementary

Converse of isosceles triangle theorem

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

Converse of the alternate interior angle theorem

If alternate interior angles are congruent, then lines are parallel

Converse of same side interior angles theorem

If same side interior angles are supplementary, then lines are parallel

Converse of corresponding angles theorem

If corresponding angles are congruent, lines are parallel

Coplanar

Points, lines, or figures that lie on the same plane

CPCTC

Corresponding parts of congruent triangles are congruent

Corresponding angles theorem

If lines are parallel, corresponding angles are congruent

Cross section

Cuts parallel to base = same shape as base, cuts perpendicular to base = shape of solid

Density

d = m/V

Diameter

Line segment that passes through the center of the circle and has both endpoints on the circumference

Dilation

Transformation enlarging or reducing a figure by a scale factor, produces a similar figure, D

Direct isometry

Rigid transformation that preserves distance and orientation

Division property of equality

If you divide both sides of an equation by the same number, both sides remain equal

Equilateral triangle

A triangle where all 3 sides are congruent and all 3 angles are congruent ( each 60 degrees )

Exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two opposite inside angles

Exterior angles

Angles formed outside a polygon when one side is extended

Exterior of an angle

An angle and its exterior are linear pairs

Chord-chord angle

Angle measure =.5( arc1 + arc2 )

General form of a circle

Not factored version

Glide reflection

Transformation that combines a slide and a reflection across a line

How to identify a base

HL Congruence

If two right triangles have a congruent hypotenuse and one corresponding leg congruent, then the triangles are congruent

Incenter

Point where all three angle bisectors meet, center of the inscribed circle, equidistant from all three sides of the triangle

Inscribed angle

An angle with its vertex on the circumference, its measure is half the measure of the intercepted arc

Inscribed quadrilaterals

Four-sided figure whose vertices lie on a circle, and opposite angles are supplementary

Intersecting chords

When two chords intersect inside a circle, the products of their segments are equal

Isometric

Transformation that preserves distance and shape

Isosceles triangle

Triangle with two congruent sides, angles opposite those sides are congruent

Isosceles triangle theorem

In an isosceles triangle, the angles opposite the two congruent sides are congruent

Isosceles trapezoid

Trapezoid with one pair of parallel sides, non-parallel sides are congruent, base angles are congruent

Kite

Has two pairs of adjacent congruent sides, perpendicular diagonals, one diagonal bisects the other, one pair of opposite angles congruent

Lateral area

Sum of all the areas of all the side faces of a 3D solid not including the base(s)

Leg rule

Leg/hypotenuse = hypotenuse segment/leg

Line symmetry

When a figure can be folded along a line so both sides match exactly

Lines perpendicular to a transversal theorem

If two perpendicular parallel lines are cut by a transversal that is perpendicular to one of them, it is also perpendicular to the other

Major arc

Arc whose measure is greater than 180 degrees

Median

Line segment from a vertex to the midpoint of the opposite side

Midpoint

Point on a line segment that divides it into two equal parts

Midpoint formula

Midpoint= (X1 + X2)/2 , (Y1 + Y2)/2

Minor arc

An arc whose measure is less than 180 degrees

Multiplication property of equality

If you multiply both sides of an equation by the same number, the equation stays equal

Net

2D flat pattern that can be folded to form a 3D solid

Obtuse angle

An angle whose measure is greater than 90 degrees

Obtuse triangle

A triangle with one obtuse angle

Opposite isometry

Transformation that preserves shape and distance but changes orientation

Orthocenter

The point where the three altitudes of a triangle intersect

Parallel chords

Stay the same distance apart, create equal arcs

Parallel lines

Lines that never intersect and stay the same distance apart

Parallelogram

Quadrilateral equal with both pairs of opposite sides parallel and congruent, opposite angles are equal, consecutive angles are supplementary, diagonals bisect each other

Partition property

When a segment is divided into parts, the sum of its parts equals the whole

Perimeter

Total distance around a shape

Perimeter of similar figures

1:1 ratio proportional by scale factor

Perpendicular lines

Two lines that intersect to form a 90 degree angle

Plane

A flat, two-dimensional surface that extends forever in all directions

Point of concurrency

The point where three or more lines, segments, or rays intersect

Point symmetry

When a figure looks the same after a 180° rotation about a point

Properties of transformations

They preserve shape size, angle measure, and distance

Proportional parts with parallel lines

When parallel lines are cut by a transversal, the segments they create are proportional

Pythagorean theorem

a² + b² = c²

Pythagorean theorem - classifying acute

a² + b² > c²

Pythagorean theorem- classifying obtuse

'a² + b² < c²

Pythagorean theorem - classifying right

a² + b² = c²

Radius - chord theorem

A radius ( or diameter ) perpendicular to a chord bisects the chord and its intercepted arc

Rectangle

A quadrilateral whose opposite sides are parallel and congruent, diagonals are congruent and bisect each other, cell four angles are right angles

Reflection in x-axis

( x, y ) → ( x, -y )

Reflection in y-axis

( x, y ) → ( -x, y )