SAT · Domain 4

Geometry and Trigonometry

15% of the SAT math section

Shapes, angles and the unit circle: about seven questions, and the ones most likely to be answered by a formula you either know or do not.

Geometry and Trigonometry · Topic 1 of 4

Lines, Angles & Similar Triangles

Angles on a straight line add to $180^\circ$ ; so do the angles of a triangle; parallel lines cut by a transversal make equal angles in matching positions. Similar triangles have equal angles and sides in one ratio — and most SAT similarity questions are a single proportion, once the sides have been matched.

The problem

Triangles

ABC

and

DEF

are similar, with

A

corresponding to

D

and

B

corresponding to

E

. If

AB = 6

,

BC = 9

and

DE = 10

, what is the length of

EF

?

A $13$
B $15$
C $5.4$
D $12$

Working1 / 3

$AB$ matches $DE$ , so the scale factor is $\frac{DE}{AB} = \frac{10}{6} = \frac{5}{3}$

Geometry and Trigonometry · Topic 2 of 4

Triangles & Trigonometry

Applying SOH CAH TOA, the special right triangles, and the relationship between the sine of an angle and the cosine of its complement. That last one appears on the test far more often than its size suggests.

The problem

In a right triangle,

\sin(x^\circ) = \frac{4}{5}

. What is the value of

\cos(90^\circ - x^\circ)

?

Working1 / 2

The cofunction identity: the sine of an angle equals the cosine of its complement $\sin(x^\circ) = \cos(90^\circ - x^\circ)$

Geometry and Trigonometry · Topic 3 of 4

Circles & Their Equations

Extracting the centre and radius from the equation of a circle, and applying arc length and area. The equation gives you $r^2$ , and most of what you are asked for wants $r^2$ — taking the root and squaring again is wasted motion.

The problem

The equation of a circle in the

xy

-plane is

(x - 3)^2 + (y + 4)^2 = 25

. What is the area of the circle?

Working1 / 4

The standard equation of a circle $(x - h)^2 + (y - k)^2 = r^2$

Geometry and Trigonometry · Topic 4 of 4

Area & Volume

The SAT gives you the formulas — a reference sheet is one click away in the test app — so it does not test whether you know them. It tests whether you use them right: a composite shape split into pieces, a unit converted before it is squared, and what happens to a volume when one dimension changes.

The problem

A right circular cylinder has a volume of

48\pi

cubic centimetres. A second cylinder has the same height and twice the radius. What is the volume, in cubic centimetres, of the second cylinder?

A $96\pi$
B $192\pi$
C $384\pi$
D $48\pi$

Working1 / 3

The volume of a cylinder $V = \pi r^2 h$