Digital SAT Math Geometry and Trigonometry Lines, angles, and triangles

📐 Geometry Topics on the Digital SAT

1. Lines and Angles

• Complementary angles: sum to 90°

• Supplementary angles: sum to 180°

• Vertical angles: congruent

• Angles on a straight line: sum to 180°

• Angles around a point: sum to 360°

2. Triangles

• Sum of interior angles: 180°

• Types: equilateral, isosceles, scalene

• Pythagorean Theorem (for right triangles):

  a2+b2=c2a^2 + b^2 = c^2a2+b2=c2

• Special Right Triangles:

  • 45°–45°–90°: sides in ratio 1:1:21 : 1 : \sqrt{2}1:1:2​

  • 30°–60°–90°: sides in ratio 1:3:21 : \sqrt{3} : 21:3​:2

3. Circles

• Radius / Diameter: $d=2r$

• Circumference: $C=2\pi r$

• Area: A=πr2A = \pi r^2A=πr2

• Arc length:

  $$\text{Arc length}=\theta /360\times 2\pi r$$

• Sector area:

  Sector area=θ/360×πr2\text{Sector area} = \theta/360 \times \pi r^2Sector area=θ/360×πr2

• Inscribed angles: half the measure of the intercepted arc

4. Polygons

• Sum of interior angles of an n-sided polygon:

  (n−2)×180∘(n – 2) \times 180^\circ(n−2)×180∘

• Interior angle of a regular polygon:

  (n−2)×180∘n\frac{(n – 2) \times 180^\circ}{n}n(n−2)×180∘​

5. Coordinate Geometry

• Distance formula:

  d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​

• Midpoint formula:

  (x1+x22,y1+y22)\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)(2x1​+x2​​,2y1​+y2​​)

• Slope:

  m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}m=x2​−x1​y2​−y1​​

📏 Trigonometry Topics on the Digital SAT

1. Basic Trig Ratios (in right triangles):

• sin⁡(θ)=oppositehypotenusecos⁡(θ)=adjacenthypotenusetan⁡(θ)=oppositeadjacent\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \quad \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \quad \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}sin(θ)=hypotenuseopposite​cos(θ)=hypotenuseadjacent​tan(θ)=adjacentopposite​

2. Trig Identities (basic ones tested):

• sin⁡2(θ)+cos⁡2(θ)=1\sin^2(\theta) + \cos^2(\theta) = 1sin2(θ)+cos2(θ)=1

• Tangent identity:

  tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}tan(θ)=cos(θ)sin(θ)​

3. Applications

• Trigonometry is often used in problems involving:

  • Heights and distances

  • Angles of elevation/depression

  • Modeling with sine and cosine functions

📌 Strategies for Success

• Memorize key formulas, especially triangle ratios and circle formulas.

• Draw diagrams—even when not provided.

• Label everything—angles, sides, coordinates.

• Use logic—some geometry problems can be solved without calculations.

• For trig, remember SOH-CAH-TOA and the basic identities.

• Be careful with units (degrees vs. radians are not emphasized on the SAT—use degrees unless told otherwise).