Geometry questions often provide more angle information than you need. Mark equal, supplementary, and complementary relationships, then connect them through triangle sums, parallel lines, or similar figures.
Essential concepts
\[A+B+C=180^circ qquad rac{a_1}{a_2}= rac{b_1}{b_2}= rac{c_1}{c_2}\]
Corresponding sides of similar triangles share one scale factor; corresponding angles are equal.
SAT strategy and application
Use the triangle angle sum
A triangle’s angles measure \(x\), \(2x\), and \(3x\). Find the angles.
- Write the sum
\(x+2x+3x=180\).
- Solve and evaluate
\(6x=180\), so \(x=30\).
Angles: \(30^circ,60^circ,90^circ\).
Mistakes and traps
Check your understanding
A triangle has remote interior angles of 45° and 70°. What is the adjacent exterior angle?
- 65°
- 70°
- 115°
- 135°
Show answer and explanation
Answer: 115°
An exterior angle equals the sum of the two remote interior angles: 45° + 70° = 115°.
Key takeaways
What to remember
- Connect vertical, supplementary, and parallel-line angle relationships.
- Use triangle sums and exterior-angle relationships efficiently.
- Establish correspondence before writing similarity proportions.
- Never infer geometric facts from appearance alone.
Continue learning
Put these notes into practice
Apply the ideas with SAT-style questions, then reinforce key details with flashcards.