Geometry Regents Exam Review Flashcards

Flashcards for Geometry Regents Exam review covering circles, factoring, triangle congruence, trigonometry, and quadrilaterals.

General/Standard Equation of a Circle

x² + y² + Cx + Dy + E = 0

Circle

A 2-dimensional shape made by drawing a curve that is always the same distance from the center.

Order of Factoring

Greatest Common Factor, Difference of Two Perfect Squares, Trinomial/'AM Method'

GCF Formula

ab + ac = a(b+c)

DOTS Formula

x² - y² = (x + y)(x - y)

Center-Radius Equation of a Circle

(x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius.

Completing the Square

Used when the basic 'Trinomial Method' or 'AM' method cannot be applied; commonly used to express a general circle equation in center-radius form.

Steps for Graphing Circles

Determine the center and the radius, plot the center, create four loci points equidistant from the center, connect the points.

SAS

Side-Angle-Side

ASA

Angle-Side-Angle

SSS

Side-Side-Side

Altitude Theorem

The altitude is the geometric mean between the 2 segments of the hypotenuse.

Leg Theorem

The leg is the geometric mean between the segment it touches and the whole hypotenuse.

AAS

Angle-Angle-Side

HL

Hypotenuse-Leg

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

AA

Angle-Angle

Angle-Angle (aa)

applies to Similar figures which , have congruent angles and proportional sides

The Pythagorean Theorem

a² + b² = c² where a and b are the legs, and c is the hypotenuse

Sine (sin)

opposite/hypotenuse

Cosine (cos)

adjacent/hypotenuse

Tangent (tan)

opposite/adjacent

Cofunctions

Sine and Cosine; they are complementary

CSSTP

Corresponding Sides of Similar Triangles are in Proportion

Sum of Interior Angles of a Polygon

180(n-2)

Sum of Exterior Angles of a Polygon

360°

Scalene Triangle

No congruent sides

Isosceles Triangle

2 congruent sides

Equilateral Triangle

3 congruent sides

Acute Triangle

All angles are < 90°

Right Triangle

One right angle that is 90°

Obtuse Triangle

One angle that is > 90°

Exterior Angle Theorem

Exterior angle is equal to the sum of the two non-adjacent interior angles

Midsegment

Segment that joins two midpoints

Slope-Intercept Form of a Line

y = mx + b

Point-Slope Form of a Line

y - y₁ = m(x - x₁)

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

Distance Formula

√((x₂ - x₁)² + (y₂ - y₁)²)

Triangle Inequality Theorem

Sum of 2 sides must be greater than the third side.

Side-Splitter Theorem

If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally.

Quadrilateral

A four-sided polygon

Trapezoid

At least one pair of parallel sides

Isosceles Trapezoid

Each pair of base angles are congruent; diagonals are congruent

Parallelogram

Opposite sides are parallel; opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other.

Rectangle

All angles are right angles; diagonals are congruent

Rhombus

All sides are congruent; diagonals are perpendicular; diagonals bisect opposite angles.

Central Angle

Central Angle measure equals its intercepted arc

Inscribed Angle

Inscribed Angle measure equals one-half of intercepted arc

Tangent-Chord Angle

Tangent-Chord Angle measure equals one-half of intercepted arc

Two Chord Angles

Two Chord Angle measure equals one-half the sum of intercepted arcs

Two Secant Angles

Angle formed by Two Secants measure is one-half the difference between the Big Arc and Little Arc

Intersecting Chords Segment Theorem

(Part)(Part) = (Part)(Part)

Two Secants Segment Theorem

(Whole)(External) = (Whole)(External)

Secant-Tangent Segment Theorem

(Whole)(External) = (Tangent)²