Every Easy SAT Geometry Question

Summary

The video walks through easy SAT geometry questions. The instructor solves examples and emphasizes recognizing the small set of rules and formulas that appear repeatedly.

Main Concepts and Methods

Congruent and Similar Triangles

• For congruent triangles, corresponding sides and angles are equal. Match the vertices in the order given.
• Similar triangles have equal corresponding angles, while their corresponding side lengths share a constant scale factor.
• To solve a shadow problem, set up a proportion between the heights and shadow lengths. Keep track of which measurements correspond.
• If all side lengths of one similar triangle are twice those of another, its perimeter is also twice as large.

Angles

• The interior angles of any triangle sum to 180°. Add the known angles and subtract from 180° to find a missing angle.
• The two acute angles in a right triangle sum to 90°.
• In an isosceles triangle, equal sides have equal opposite angles.
• Vertical angles are equal.
• A linear pair—two adjacent angles forming a straight line—sums to 180°.
• For parallel lines cut by a transversal:
  • Corresponding angles are equal.
  • Alternate interior angles are equal.
  • Some related angles form linear pairs and are supplementary.
  • Check whether angles are acute or obtuse to help distinguish equal angles from supplementary ones.
• An exterior angle of a triangle equals the sum of the two nonadjacent interior angles.

Area, Perimeter, and Volume

• Rectangle area: (A = \text{length} \times \text{width}).
• Square area: (A = s^2). If the area is given, take its positive square root to find the side length.
• Triangle area: (A = \frac{1}{2}bh).
• Rectangle perimeter: (P = 2l + 2w).
• Square perimeter: (P = 4s).
• Triangle perimeter is the sum of its three sides; use the given perimeter to solve for a missing side.
• When part of a figure is removed, subtract its area from the original area.
• Rectangular-prism volume: (V = lwh).
• Keep units straight: area uses square units, volume uses cubic units, and perimeter uses ordinary length units.

Right Triangles and Trigonometry

• Pythagorean theorem: (a^2 + b^2 = c^2), where (c) is the hypotenuse. Take the positive square root when solving for a length.
• The hypotenuse is the longest side. The triangle inequality can help rule out impossible answer choices.
• Use SOH-CAH-TOA:
  • (\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}})
  • (\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}})
  • (\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}})
• The video’s examples focus on sine and tangent.

Circles and Arcs

To find an arc length, determine what fraction of the full circle the arc represents, then multiply that fraction by the circumference. For example, a 90° arc is one-quarter of a circle, so its length is one-quarter of the circumference.

Test-Taking Advice

• Read carefully to determine whether the question asks for area, perimeter, volume, an angle, or a side length.
• Track corresponding vertices and sides in triangle problems.
• Sketching a quick diagram can help organize information, but do not assume a diagram is drawn to scale.
• Use answer choices and estimation to eliminate impossible values.
• A calculator is available on the SAT, but knowing the relationships and formulas helps avoid setup errors.

Speakers and Sources Featured

• Mr. McGrinder — the instructor and narrator.
• Bubba, the instructor’s dog — briefly heard or mentioned; not an instructional speaker.
• SAT Online Question Bank / College Board — the source of the geometry questions referenced by the instructor.