Lines, angles, and triangles
Most SAT geometry problems in this topic reduce to identifying the angle relationship or triangle rule, then writing the equation it creates.
Core Idea
Angle relationships and triangle properties are the building blocks of SAT geometry. Most problems come down to knowing a few key rules — vertical angles are equal, angles in a triangle sum to 180°, and similar triangles have proportional sides — and chaining them together.
Understanding
Rule: Match the angle pattern first, then write the equation.
- Parallel lines give you equal or supplementary angle pairs.
- Triangle facts give you
1 8 0 ∘ - Similar triangles turn matching sides into proportions.
Most mistakes come from picking the right rule for the wrong angle pair.
Concept Guides
6Use angle relationships (vertical angles; angles formed by parallel lines and a transversal).
Vertical, corresponding, alternate interior, and same-side interior angles are the key line-angle re
Apply triangle angle-sum and related theorems to find unknown angles.
Use the triangle angle sum or the exterior-angle theorem to find unknown angles.
Use properties of isosceles and equilateral triangles.
Use the equal base angles of isosceles triangles and the 60° angles of equilateral triangles.
Use congruence and similarity concepts to solve for side lengths/angles.
Know when triangles are congruent or similar: congruent triangles match exactly, while similar trian
Use scale factor properties (changes lengths but not angles).
Scaling changes lengths by the factor, area by its square, and leaves angles unchanged.
Solve multistep geometry problems involving lines, angles, and triangles.
Chain one geometry rule into the next when a problem needs more than one step.