Lesson 1: Similar Triangles

• Characteristics of similar triangles

  • Expressing similar triangles

  • Proportional triangles and their expressions

  • Conditions for similarity

• Types of similarities

  • SSS

  • SAS

  • AA

• Congruent triangles

  • Identifying congruent triangles

  • Characteristics of congruent triangles

  • Conditions for congruence

• Types of Congruence

  • SSS

  • SAS

  • ASA

Lesson 2: Triangles and Their Relationships

• Triangles and angle relationships

• Properties of triangles and relationships

  • Complementary

  • Isosceles; Supplementary; and External angles

  • Transversal and parallel lines

• Corresponding and Co-interior angles

Lesson 3: Introduction to Trigonometry

• Investigating right triangles

  • Pythagorean Theorem

  • Primary trigonometric ratios

  • Relating the opposite and adjacent with an angle

  • Identifying SOH, CAH, and TOA

• Solving questions using trigonometric ratios

  • Solving for a side

  • Solving for an angle (use of sin-1, cos-1, and tan-1)

  • Technique for solving these questions

  • Caution to ensure accuracy (proper use of calculator)

Lesson 4: Non- Right Angle Triangles

• The sine rule (method 1)

  • Understanding sides and angles in relation to angles

  • Sine rule formula

  • Two conditions for sine rule

  • Solving application questions with sine rule

  • Drawing diagrams to represent questions

  • Caution for final answers

• The cosine rule (method 2)

  • The cosine rule formula

  • Understanding the pattern of the formula

  • Key to remembering the formula

  • Two conditions for cosine rule

  • Understanding the “joining” angle

  • Solving for unknown side using cosine rule

  • Solving for unknown angle using cosine rule

  • Applying cosine rule for triangles PQR or MNO etc.

Here are a few sample questions for you to practice. The answers are given at the end.