Lines, Angles, Triangles — Digital SAT SAT Math revision notes
A 3-page visual revision sheet for Lines, Angles, Triangles, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Lines, Angles, Triangles in one look
two values in the whole picture, and a ratio that never changes
Two parallel lines cut by one transversal
- the chevrons are the notation for parallel. Without them, or without the question saying so, nothing below is allowed
- eight angles appear, but only two different values: some angle x, and its supplement 180-x. Four angles take each value
- equal to each other are the vertically opposite pair at one crossing, the corresponding pair (same position at both crossings) and the alternate interior pair (opposite sides, between the lines)
- any two angles that are NOT equal here are supplementary, so they add to 180
Worked: two expressions for one angle
Q. line L_1 is parallel to line L_2. A transversal makes a pair of alternate exterior angles measuring (3x+12) and (5x-24) degrees. What is the obtuse angle formed?
- alternate exterior angles on parallel lines are equal, so 3x+12=5x-24
- 36=2x, giving x=18
- each of those angles is 3(18)+12=66°, and 5(18)-24=66° agrees
- 66 is acute, so the obtuse angle at the same crossing is its supplement: 180-66
Answer: the obtuse angle is 114°
Triangle rules worth carrying
- the three angles of any triangle
a+b+c=180° - an exterior angle equals the two remote interior ones
e=a+b - isosceles: equal sides face equal angles
AB=AC⇒ B=C - similar triangles, every pair of matching sides in one ratio
DE/AB=EF/BC=k - perimeter scales the same way a single length does
P_2=kP_1
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Lines, Angles, Triangles sheet covers
- Two parallel lines cut by one transversal
- Worked: two expressions for one angle
- Triangle rules worth carrying
- the three angles of any triangle
- an exterior angle equals the two remote interior ones
- isosceles: equal sides face equal angles
- similar triangles, every pair of matching sides in one ratio
- perimeter scales the same way a single length does
- The four names, and the shape each one makes
- Vertically opposite
- Corresponding
- Alternate interior
- Co-interior
- Worked: angles in a ratio
- Worked: an exterior angle
- Similar triangles: one ratio, every length
- triangle ABC
- triangle DEF
- Pacing, the sheet and the figures
- Symbols and terms
- Traps that cost points
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Lines, Angles, Triangles the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.
More SAT Math revision notes
- Area and Volume
- Circles
- Equivalent Expressions and Polynomials
- Evaluating Statistical Claims
- Inference and Margin of Error
- Linear Equations
- Linear Functions
- Linear Inequalities
- Nonlinear Equations in One Variable
- Nonlinear Functions
- Nonlinear Systems
- One-variable Data
- Percentages
- Probability and Conditional Probability
- Ratios, Rates and Proportions
- Systems of Equations
- Triangles and Trigonometry
- Two-variable Data
- Units, Rates and Conversions