Geometry Brain Dump – First Semester

Flashcards for Geometry First Semester

Pythagorean Theorem

𝑎² + 𝑏² = 𝑐²

Slope-Intercept Form

𝑦 = 𝑚𝑥 + 𝑏

Point-Slope Form

𝑦 − 𝑦₁ = 𝑚(𝑥 − 𝑥₁)

Linear Pair

Sum of 180°, forms straight line

Supplementary Angles

Sum of 180°

Complementary Angles

Sum of 90°

Acute Angle

Less than 90°

Right Angle

90°

Obtuse Angle

In between 90° and 180°

Straight Angle

180°

Vertical Angles

Congruent, equal measures

Alternate Interior Angles

Congruent, equal measures

Alternate Exterior Angles

Congruent, equal measures

Corresponding Angles

Congruent, equal measures

Same Side (Consecutive) Interior Angles

Sum of 180°

Same Side (Consecutive) Exterior Angles

Sum of 180°

90° Clockwise Rotation

(𝑥, 𝑦) → (𝑦, −𝑥)

90° Counterclockwise Rotation

(𝑥, 𝑦) → (−𝑦, 𝑥)

180° Rotation

(𝑥, 𝑦) → (−𝑥 , −𝑦)

Reflection over x-axis

(𝑥, 𝑦) → (𝑥, −𝑦)

Reflection over y-axis

(𝑥, 𝑦) → (−𝑥, 𝑦)

Reflection over 𝑦 = 𝑥

(𝑥, 𝑦) → (𝑦, 𝑥)

Reflection over 𝑦 = −𝑥

(𝑥, 𝑦) → (−𝑦, −𝑥)

Dilation

(𝑥, 𝑦) → (𝑘𝑥, 𝑘𝑦) where k is the scale factor

Right Triangle

One right angle

Acute Triangle

Three acute angles

Obtuse Triangle

One obtuse angle

Equiangular Triangle

All 60° angles

Isosceles Triangle

Two congruent sides/angles

Scalene Triangle

No congruent sides/angles

Equilateral Triangle

Three congruent sides

Side-Side-Side (SSS) Congruence

All three sides of one triangle are congruent to the corresponding sides of another triangle.

Side-Angle-Side (SAS) Congruence

Two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle.

Angle-Side-Angle (ASA) Congruence

Two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle.

Angle-Angle-Side (AAS) Congruence

Two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle.

Hypotenuse-Leg (HL) Congruence

The hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and leg of another right triangle.

Angle-Angle (AA~) Similarity

Two angles of one triangle are congruent to two angles of another triangle.

Side-Side-Side (SSS~) Similarity

All three sides of one triangle are proportional to the corresponding sides of another triangle.

Side-Angle-Side (SAS~) Similarity

Two sides of one triangle are proportional to the corresponding sides of another triangle, and the included angles are congruent.

Rigid Transformations

Translations, Reflections, Rotations. Preserve Distance

Non-Rigid Transformation

Dilations. Does Not Preserve Distance if scale factor is not 1

Conditional Statement

p → q

Converse

q → p

Inverse

~p → ~q

Contrapositive

~q → ~p

Biconditional

p ↔ q