Are SAT figures drawn to scale?

On the digital SAT, figures are drawn to scale unless a note says otherwise. Treat scale as a sanity check, not a solving method: your answer should come from the marked values and the theorems, then agree with the picture.

How do I spot similar triangles quickly?

Look for a line parallel to one side of a triangle, two triangles sharing an angle, or parallel lines crossed by two transversals. Parallel markings are the SAT's favorite similarity signal.

What is the exterior angle theorem?

An exterior angle of a triangle equals the sum of the two remote interior angles. It replaces two rounds of 180° arithmetic with one addition, which is exactly why fast solvers lean on it.

How many questions come from this skill?

Geometry and Trigonometry covers about 15 percent of SAT Math, roughly 7 of the 44 questions across the two 35 minute modules, and angle and triangle reasoning typically claims 1 to 2, plus cameos inside trig and circle questions.

What makes these drills worth repeating?

The generators redraw the figure with new givens on every load, so you practice choosing the right theorem instead of recalling that one answer was 110°. All 1,483 questions in the bank are independently verified.

Geometry and Trig · Skill 2 of 4

SAT Lines, Angles, and Triangles Practice

Angle chasing is the digital SAT's favorite way to test whether you see structure: parallel lines, triangle sums, and similarity stacked into one figure. Every one of these questions falls to the same handful of theorems applied in the right order, and this page drills that order until it is automatic.

Domain: Geometry and Trig
About 15% of the test is Geometry and Trig
Difficulty: easy to hard
Free, no account

Drill angle chasing now → See all Geometry and Trig skills

The patterns the SAT actually uses

Four patterns, a handful of theorems. The figures grow more tangled at hard difficulty, but the toolkit never gets bigger.

Pattern 01

Parallel lines and a transversal

Alternate interior, corresponding, and same side angles. Every zigzag figure is this pattern in disguise: extend the lines and the equal pairs appear.

Pattern 02

Chase angles through triangles

Angles in a triangle sum to 180°, and an exterior angle equals the sum of the two remote interior angles. Chaining those two facts carries you across any figure.

Pattern 03

Set up similarity

A line parallel to one side of a triangle, or two triangles sharing an angle. Match corresponding sides carefully, write one proportion, cross multiply once.

Pattern 04

Use the tick marks

Equal side markings flag isosceles triangles, and equal base angles ride along free. Many hard figures are one isosceles observation followed by a single 180° step.

One worked example, start to finish

Worked example · medium

In triangle ABC, point D lies on side AB and point E lies on side AC so that segment DE is parallel to segment BC. AD = 6, DB = 4, and AE = 9. What is the length of segment EC?

DE parallel to BC makes triangle ADE similar to triangle ABC: they share angle A, and the parallel line copies the other two angles across.
Match whole sides with whole sides: AD/AB = AE/AC. Since AB = 6 + 4 = 10, the proportion reads 6/10 = 9/AC.
Cross multiply: 6 × AC = 90, so AC = 15. Then EC = AC − AE = 15 − 9 = 6.
Check with the splitter shortcut: a parallel line cuts both sides in the same ratio, and AD/DB = 6/4 = 3/2 while AE/EC = 9/6 = 3/2. It matches.

Answer: EC = 6

The letters and lengths change on every load. Parallel means similar, whole matches whole, one proportion finishes it.

Where students lose the point

Pairing wrong sides in similar triangles. AD matches AB, whole side with whole side. Mixing a piece with a whole, like AD with DB, builds a proportion that solves cleanly to a planted wrong answer.
Trusting looks over givens. Scale can confirm an answer, but the credited reasoning runs through marked values and theorems. An angle that looks like 90° is not 90° until something says so.
Misusing the exterior angle. An exterior angle equals the sum of the two remote interior angles, not the sum of any two angles, and never 180° plus anything.
Forgetting the triangle inequality. The third side lies strictly between the difference and the sum of the other two. Choices equal to those exact bounds are traps, not answers.

Using Desmos here

Angle chasing happens in your head and on scratch paper, not in a graphing window, so this is a light Desmos skill. Where the calculator earns its keep is checking proportions: type 6/10 and 9/15 and confirm both equal 0.6 before you commit to a similarity answer. Treat Desmos as a fraction checker and keep the geometric reasoning for yourself, because that is what the question is actually grading.

Why drilling here is different

Each load of these drills redraws the figure: new angle measures, new parallel line setups, new similarity chains, at all three difficulty levels. You practice choosing the theorem, not recalling the diagram. All 1,483 questions in Satified's bank carry independently verified answers and explanations.

A fresh figure, every single load.

Start this skill free →

Questions students ask

Are SAT figures drawn to scale?: On the digital SAT, figures are drawn to scale unless a note says otherwise. Treat scale as a sanity check, not a solving method: your answer should come from the marked values and the theorems, then agree with the picture.
How do I spot similar triangles quickly?: Look for a line parallel to one side of a triangle, two triangles sharing an angle, or parallel lines crossed by two transversals. Parallel markings are the SAT's favorite similarity signal.
What is the exterior angle theorem?: An exterior angle of a triangle equals the sum of the two remote interior angles. It replaces two rounds of 180° arithmetic with one addition, which is exactly why fast solvers lean on it.
How many questions come from this skill?: Geometry and Trigonometry covers about 15 percent of SAT Math, roughly 7 of the 44 questions across the two 35 minute modules, and angle and triangle reasoning typically claims 1 to 2, plus cameos inside trig and circle questions.
What makes these drills worth repeating?: The generators redraw the figure with new givens on every load, so you practice choosing the right theorem instead of recalling that one answer was 110°. All 1,483 questions in the bank are independently verified.

Keep going

Angle and triangle reasoning is the backbone of the two skills that follow, trigonometry and circles.