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Math · Checkpoint 21 of 30 · Geometry and Trigonometry · ~13 min
Geometry: lines, angles & triangles
Angle relationships, similar triangles, and the Pythagorean theorem.
The 30-second version
three tools solve most SAT triangle questions. (1) Angles: straight line = 180°, triangle = 180°, vertical angles equal, parallel lines cut by a transversal repeat the same two angle values everywhere. (2) Similar triangles: same angles → sides in proportion — set up the ratio. (3) Right triangles: a² + b² = c². The skill is spotting which tool the figure is hiding.
Learn it
Angle chasing
Most angle problems fall to patient bookkeeping: mark what you know, then apply "straight line = 180," "triangle = 180," and "vertical angles are equal" until the target falls out. With parallel lines, every angle formed is either x or 180 − x — label one angle and propagate. An exterior angle of a triangle equals the sum of the two remote interior angles (a one-step shortcut worth memorizing).
Similar triangles
Two triangles with equal angles are scaled copies: corresponding sides share one ratio. The SAT's favorite disguise is a triangle inside a triangle — a line parallel to one side creates a smaller similar triangle sharing a vertex. Match corresponding sides carefully (shortest with shortest), write small/big = small/big, cross-multiply.
Right triangles and Pythagoras
a² + b² = c², hypotenuse always the longest side, opposite the right angle. The famous integer triples — 3-4-5, 5-12-13, and their multiples (6-8-10, 9-12-15, 10-24-26) — appear constantly; recognizing one saves 30 seconds of arithmetic. Distance between two points on a coordinate grid is the same theorem: legs are the horizontal and vertical gaps.
Common traps
- Assuming a right angle that isn't marked. Figures suggest; only the little square (or the words) guarantees.
- Mismatching corresponding sides in similar triangles — pair sides by the angles they face, not by picture position.
- c² is the hypotenuse's square. Given a leg and hypotenuse, subtract: b² = c² − a².
Try it
A 13-foot ladder leans against a wall with its base 5 feet from the wall. How high on the wall does it reach?
Ladder = hypotenuse (13), base = leg (5): height² = 13² − 5² = 169 − 25 = 144 → 12. It's the 5-12-13 triple. B comes from adding instead of subtracting (13² + 5²) — the treat-everything-as-a-leg mistake.
Free resources for this checkpoint
Khan Academy Official Digital SAT Prep (opens in a new tab)
Free structured lessons, video instruction, and practice exercises for both SAT sections, built with College Board as the official practice partner. After a Bluebook practice test, you can link your results to get personalized practice recommendations.
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Practice next
Question Bank filter: Math → Geometry and Trigonometry → Lines, angles, and triangles. Redraw messy figures on scratch paper — half of geometry is a cleaner diagram.
Practice these skillsOriginal Digital SAT-style questions on what this checkpoint covers.