Geometry and Trigonometry

Five topics covering the SAT's Geometry and Trigonometry domain end to end. Lines, angles, and triangles, right triangles, right-triangle trigonometry, circles, and area and volume. The errors here are setup errors: the wrong angle rule, a misplaced hypotenuse, a ratio built from the wrong sides, a diameter posing as a radius.

Topics

5.1

Lines, Angles, and Triangles

Right Triangles

Right-Triangle Trigonometry

Circles

Area and Volume

Lesson

Diagnostic

after diagnostic

Reference The triangle, circle, and trig facts behind every problem in this unit

Right triangle (hypotenuse sits alone)

$a^{2} + b^{2} = c^{2}$

Special triangles (from the short side)

$x,\ x,\ x\sqrt{2} \quad\text{and}\quad x,\ x\sqrt{3},\ 2x$

Trig ratios (from the named angle)

$\sin = \dfrac{\text{opp}}{\text{hyp}},\ \cos = \dfrac{\text{adj}}{\text{hyp}},\ \tan = \dfrac{\text{opp}}{\text{adj}}$

Cofunction (complements, through 90)

$\sin x^{\circ} = \cos(90 - x)^{\circ}$

Circle (radius, never diameter)

$A = \pi r^{2}, \quad C = 2\pi r, \quad (x - h)^{2} + (y - k)^{2} = r^{2}$

Arc and sector (share of the right whole)

$\dfrac{\theta}{360}\cdot 2\pi r \quad\text{and}\quad \dfrac{\theta}{360}\cdot \pi r^{2}$

Unit 5 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Mixed items pulled from across the unit's topics, with no labels showing which is which. It surfaces the misconceptions that still bite when you cannot tell what a question is testing.