SAT Prep – Math: Geometry + Trigonometry

DSAT Math Content: Geometry and Trigonometry Domain

The digital SAT includes fewer geometry questions than the old SAT, but foundational knowledge is still required. A built‑in reference sheet provides essential formulas.

Core Skills:

  • Area and perimeter of polygons
  • Circles: radius, diameter, arc lengths
  • Coordinate geometry (slope, midpoint, distance)
  • Volume of cylinders, cones, spheres
  • Right‑triangle trigonometry
  • Transformations and geometric reasoning

Example

sat-geometry-trigonometry-1

In the given figure above, $AB{\parallel}EF$, $CD{\parallel}GH$ and points P, Q and R are intersection points of the lines. If $\angle APC=20$°, what is the measurement of $\angle GRF$ (in degrees)?

Solution

As $AB{\parallel}EF$, $\angle APC=\angle EQC$ (corresponding angles) ... (1)

Now, $\angle EQC=\angle DQF$ (vertically opposite angles) ... (2)

Also, $CD{\parallel}GH$. So, $\angle DQF=\angle GRF$ (corresponding angles) ... (3)

From equation (1), (2) and (3); we can say that $\angle APC=\angle GFR$

As, $\angle APC=20$°

Hence, $\angle GFR=20$°

The correct answer is 20.

Applications:

  • Engineering and Architecture
  • Navigation and Mapping
  • Physics and Motion
  • Everyday Quantitative Tasks

Tools on SAT:

  • Reference sheet for geometry formulas
  • Built‑in graphing calculator