Unit 5 of 6

Geometry and Trigonometry

  • 11 lessons
  • Parts 93 to 114

The geometry on the SAT rests on a short list of facts about angles, triangles and circles. This unit covers angle relationships, similar and congruent triangles, the Pythagorean theorem and the special right triangles, and the sine, cosine and tangent of acute angles.

It continues with radians and the unit circle, circle theorems about angles, chords and tangents, arc length and sector area, equations of circles, and area, volume and surface area, including how they change when a figure is scaled.

Every lesson is a pair of videos. The theory part explains the idea and the practice part works through problems. Each lesson page has the definitions and an example for every key term.

Lines, Angles and Triangles

  1. Angles, Parallel Lines and Triangles

    How to find unknown angles with vertical, supplementary, corresponding and alternate angles, when each relationship applies, and why the angles of a triangle add up to 180 degrees.

    Theory part 93Practice part 94

  2. Similar and Congruent Triangles

    How to match the vertices of two triangles, use AA, SSS and SAS to show they are similar or congruent, find missing lengths with a scale factor, and tell when the given facts are not enough.

    Theory part 95Practice part 96

  3. The Pythagorean Theorem and Special Right Triangles

    How to spot the hypotenuse of a right triangle, use the Pythagorean theorem to find a missing side, and write exact sides of 45-45-90 and 30-60-90 triangles.

    Theory part 97Practice part 98

Right Triangle Trigonometry and the Unit Circle

  1. Sine, Cosine and Tangent in Right Triangles

    How to name the opposite and adjacent sides for a chosen acute angle, why sine, cosine and tangent depend only on the angle, and how to use them and complementary angles to find sides.

    Theory part 99Practice part 100

  2. Degrees, Radians and the Unit Circle

    What a radian measures, how to convert between degrees and radians, why arc length is radius times angle in radians, and how angles give the cosine and sine coordinates of points on the unit circle.

    Theory part 101Practice part 102

Circles

  1. Circle Angles, Chords and Tangents

    How central and inscribed angles relate to the arcs they intercept, why a tangent is perpendicular to the radius, and how a chord, its distance from the center and the radius form a right triangle.

    Theory part 103Practice part 104

  2. Arc Length and Sector Area

    How the central angle tells you what fraction of a circle you have, and how that one fraction gives both the arc length and the sector area, in degrees or in radians.

    Theory part 105Practice part 106

  3. Circle Equations, Centers and Radii

    How the equation of a circle comes from the distance formula, how to read its center and radius, and how to recover them by completing the square or from the endpoints of a diameter.

    Theory part 107Practice part 108

Area, Volume and Scaling

  1. Area, Perimeter and Composite Figures

    How to find the area of an odd shape by splitting it into simple pieces or subtracting a piece, why a triangle needs its perpendicular height, and how perimeter differs from area.

    Theory part 109Practice part 110

  2. Volume and Surface Area

    How to tell whether a question asks for the space inside a solid or the surfaces around it, and how to find volume and surface area for prisms, cylinders, pyramids, cones and spheres.

    Theory part 111Practice part 112

  3. Scaling Lengths, Areas and Volumes

    Why multiplying every length of a shape by k multiplies its area by k squared and its volume by k cubed, and how to run that rule backward from an area or volume ratio.

    Theory part 113Practice part 114