Math for Coffee: Geometry Final Exam Review

Introduction

• Presenter: Tammy
• Focus: Review of 20 topics likely to appear in a first semester geometry final exam.
• Structure: Topics covered in order with time stamps available for navigation.

Segment Addition Postulate

• Objective: Find the length of segment PQ.
• Given:
  • Length of P to R = 19.
  • Equation: ( 2x - 2 + 2x - 7 = 19 )
• Solution:
  • Combine like terms: ( 4x - 9 = 19 )
  • Solve: ( 4x = 28 ), ( x = 7 )
  • Calculate PQ: ( 2(7) - 2 = 12 )

Angle Addition Postulate

• Objective: Solve for x given angles ARQ, SRA, and SRQ.
• Given:
  • ( \angle ARQ = x + 45 )
  • ( \angle SRA = x + 86 )
  • ( \angle SRQ = 109 )
• Solution:
  • ( x + 45 + x + 86 = 109 )
  • Solve: ( 2x + 131 = 109 ), ( x = -11 )

Vocabulary: Angle Relationships

• Key Terms: Complementary, Linear Pair, Vertical, Adjacent
• Example: Two angles A and B are complementary if they add up to 90 degrees.

Central Angles

• Entire circle = 360 degrees.
• Example Problem:
  • Given angles: 227, B, and 69.
  • Equation: ( 227 + B + 69 = 360 )
  • Solution for B: ( B = 64 )

Complementary Angles

• Equation: ( 3x + 2 + 40 = 90 )
• Solution:
  • Solve for x: ( x = 16 )
  • Verification: Substitute ( x ) back to check total = 90.

Angle Bisectors

• Definition: Splits angles in half.
• Example:
  • ( \angle 1 = 17x ), ( \angle 2 = 18x - 1 )
  • Equation: ( 17x = 18x - 1 )
  • Solution: ( x = 1 )

Parallel Lines and Transversals

• Example Problem:
  • Determine X and Y: Same Side Interior Angles
  • Making lines parallel: Angles must be supplementary (add up to 180).

Triangle Classification

• By sides: Equilateral, Isosceles, Scalene
• By angles: Acute, Right, Obtuse
• Example: Scalene acute triangle

Triangle Sum Theorem

• All angles in a triangle sum to 180 degrees.
• Example: ( x + 87 + 31 = 180 )
• Solution: ( x = 62 )

Exterior Angle Theorem

• Exterior angle equals sum of two opposite interior angles.
• Example solution: ( 61 + 30 = 91 )

Isosceles Triangles

• Base angles are congruent.
• Example: Solving for angle measures in isosceles configurations.

Pythagorean Theorem and Its Converse

• Theorem: ( c^2 = a^2 + b^2 )
• Converse: Determines if triangle is right, acute, or obtuse based on side lengths.

Congruent Triangles

• Proof techniques: ASA (Angle-Side-Angle), SAS (Side-Angle-Side)
• Example: Verifying triangle congruence and required conditions

Quadrilaterals

• Angle Sum: 360 degrees.
• Parallelograms: Consecutive angles sum to 180.
• Diagonals bisect each other.

Practice and Further Study

• Suggested practice links available for more in-depth exploration of topics.