ryanagnos01_geometry-semester-1

Page 1: Geometry Semester 1 Cheat Sheet

Important Formulas

  • Distance Formula: Used to calculate the distance between two points in a plane.

  • Slope Formula: Used to find the slope of a line given two points.

  • Midpoint Formula: Determines the midpoint between two points.

Types of Angles

  • Acute Angle: Less than 90°.

  • Right Angle: Equal to 90°.

  • Obtuse Angle: More than 90° but less than 180°.

  • Straight Angle: Equal to 180°.

Angle Relationships

  • Adjacent Angle: Two angles that share a common side and vertex.

  • Complementary Angles: Two angles whose measures add up to 90°.

  • Vertical Angles: Formed by the intersection of two lines; they are equal.

  • Linear Pair: A pair of adjacent angles whose non-shared sides form a straight line.

Points and Lines

  • Collinear Points: Points that lie on the same line.

  • Ray: A portion of a line that starts at a point and extends infinitely in one direction.

Types of Triangles

  • Isosceles Triangle: At least two sides are congruent.

  • Scalene Triangle: No sides are congruent.

  • Equilateral Triangle: All sides are congruent.

Proofs and Logic

  • Biconditional Statement: A statement that shows A implies B and B implies A.

  • Counterexample: An example that disproves a statement or proposition (e.g., the prime number 2 disproves "All prime numbers are odd.").

  • Isometry: A transformation that preserves distance and size.

Transformations

  • Preimage: The original figure before a transformation.

  • Translation: Moving a figure without changing its size or orientation.

Page 2: Advanced Geometry Concepts

Pythagorean Theorem

  • States that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

Congruent Angles

  • Angles that have the same measure.

Reflections

  • A transformation that flips a figure over a line to create a mirror image.

Proof Properties

  • Techniques and properties used in geometric proofs, focusing on the structure and logical sequence of statements to establish truth.

Additional Notes

  • This cheat sheet was created by ryanagnos01 and published on cheatography.com on December 19, 2017.

  • Last updated on the same date.