(1) Geometry Final 2026 Quadrilaterals, Similar Triangles, Right Triangles, Area of Polygons, Circles stuff :)

for study :)

Base angle theorem

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

Parallelogram definition

A quadrilateral with both pairs of opposite sides parallel

Parallelogram properties

Opposite sides congruent, opposite angles congruent, consecutive angles supplementary, diagonals bisect each other

Parallelogram diagonal properties

Diagonals bisect each other

Parallelogram side properties

Opposite sides congruent

Parallelogram angle properties

Opposite angles congruent, consecutive angles supplementary

Equiangular

All angles equal

Rectangle definition

Equiangular parallelogram

Rectangle properties

All angles congruent at 90°, diagonals congruent, opposite sides congruent

Rectangle diagonal properties

Diagonals are congruent

Rectangle side properties

Opposite sides congruent

Rectangle angle properties

All angles congruent at 90°

Equilateral

All sides congruent

Rhombus definition

Equilateral parallelogram

Rhombus properties

All sides congruent, opposite angles congruent, consecutive angles supplementary, diagonals perpendicular and angle bisectors

Rhombus diagonal properties

Diagonals perpendicular and angle bisectors

Rhombus side properties

All sides congruent

Rhombus angle properties

Opposite angles congruent, consecutive angles supplementary

Regular

All angles and sides congruent

Square definition

Regular parallelogram

Square properties

All sides congruent, all angles congruent, diagonals perpendicular, angle bisectors, and congruent

Square diagonal properties

Diagonals perpendicular, angle bisectors, and congruent

Square side properties

All sides congruent

Square angle properties

All angles congruent

Trapezoid definition

A quadrilateral with exactly one pair of opposite sides parallel

Trapezoid bases

Parallel sides

Trapezoid legs

Non‑parallel sides

Trapezoid midsegment

Segment parallel to each base with endpoints at midpoints of legs; length is average of bases

Isotrap definition

A trapezoid with congruent legs

Isotrap base angles

Angles that border each base; each pair is congruent

Isotrap diagonal properties

Diagonals are congruent

Kite definition

A quadrilateral with two different pairs of consecutive sides congruent

Kite diagonal properties

Longer diagonal bisects angles; diagonals perpendicular

Parallelogram angle sum

360 degrees

AA similarity

Two angles congruent

SSS similarity

All side ratios equal

SAS similarity

Two sides proportional and included angle congruent

How to show triangles similar

Match corresponding angles and compare side ratios

Similarity statement

Write triangle names in matching order with similarity symbol

Scale factor

Ratio of corresponding side lengths

Find scale factor

Choose one pair of corresponding sides

Find missing sides using similarity proportions

Set proportion, cross‑multiply, use scale factor

Pythagorean theorem

a² + b² = c²

Trigonometry acronym

SOH CAH TOA

When to use trigonometry

Use positive trig for missing sides; negative trig for missing angles

Multiply or divide in trig

Multiply when x is on top; divide when x is on bottom

45‑45‑90 rule

Leg to hyp multiply by √2

30‑60‑90 rules

Small to medium multiply by √3; small to hyp multiply by 2

Right triangle word problem steps

Draw right triangle, label values, solve with trig

Area of equilateral triangle

s²√3 / 4

Steps area equilateral triangle

Draw triangle, use SRTs for side, plug into formula

Area of square

s²

Steps for area square

Draw square, find side using SRTs, plug into formula

Area polygon 5+ sides

a × p / 2

Steps area polygon 5+ sides

Fill PAXSONR, draw right triangle, find O, solve parts, plug into formula

Polygon sum of interior angles equation

(n − 2) × 180

Polygon one interior angle equation

(n − 2) × 180 ÷ n

PAXSONR O angle equation

((n − 2) × 180 ÷ n) ÷ 2

PAXSONR

P-Perimeter, A-apothem, X-half side length, S-side length, O-O Bottom right angle, N-number of sides, R-radius

Apothem polygon

center to side

Radius polygon

center to corner

Perimeter equation

Side length × number of sides

Elevation and depression

Congruent and bottom right

If only given portion of side in right triangle word problem

Create two trig equations, isolate variable, combine

Pentagon

5 sided polygon

Hexagon

6 sided polygon

Heptagon

7 sided polygon

Octagon

8 sided polygon

Nonagon

9 sided polygon

Decagon

10 sided polygon

Tangent line is

Perpendicular to a radius

Tangent test

Use Pythagorean theorem; equal means tangent

Intersecting tangents

Congruent

Circumscribed polygon around circle

All sides tangent

Intersecting chords

Part × part = part × part

Intersecting secants

Outside × whole = outside × whole

Intersecting Secant and tangent

Tan² = outside × whole

Circle

All points equidistant from center

circle Radius

Segment on center and circle

Chord

Segment with endpoints on circle

Diameter

Chord through center

Secant

Line intersecting circle twice

Tangent

Line intersecting circle once

Point of tangency

Point where tangent intersects circle

Central angle

Vertex at center, 2 radii sides

Inscribed angle

Vertex on circle, 2 chord sides

Arc

Portion of circle edge defined by 2 endpoints

Minor arc

Arc less than 180°

Major arc

Arc greater than 180°

Semicircle

Arc with endpoints on diameter

Circle area

A = πr²

Circumference

C = 2πr or C = πd

Angle intercepting diameter

Right angle

Angles intersecting same arc

Congruent

Inscribed quadrilateral in circle

Opposite angles supplementary

Inscribed angle measure

Half arc

Central angle measure

Equals arc

Angle inside circle

Average of arcs

Angle outside circle

Half difference of arcs

Chord tangent intersection

Each angle in linear pair is half corresponding arc