SAT Math Essentials: Geometry Review

Geometry Vocabulary

• Acute Angle: An angle that measures less than 90 degrees.
• Acute Triangle: A triangle with all angles less than 90 degrees.
• Adjacent Angles: Two angles sharing a vertex and a side.
• Angle: Formed by two rays with a common endpoint.
• Arc: A curved section of a circle.
• Area: Number of square units inside a shape.
• Bisect: Divide into two equal parts.
• Central Angle: An angle formed by an arc in a circle.
• Chord: A segment with endpoints on a circle.
• Circumference: Distance around a circle.
• Complementary Angles: Two angles whose sum is 90 degrees.
• Congruent: Identical in shape and size.
• Coordinate Plane: A grid divided by x and y axes.
• Diagonal: A line segment between non-adjacent vertices of a polygon.
• Diameter: A chord passing through the center of a circle.
• Equiangular Polygon: All angles equal.
• Equilateral Triangle: A triangle with equal sides and angles.
• Exterior Angle: Formed outside a triangle or transversal.
• Hypotenuse: Opposite the right angle in a triangle, longest side.
• Interior Angle: Inside a triangle or transversal.
• Isosceles Triangle: Two equal sides.
• Line: Continues infinitely in both directions.
• Line Segment: A part of a line between two points.
• Major Arc: Arc greater than 180 degrees.
• Minor Arc: Arc less than 180 degrees.
• Obtuse Angle: An angle greater than 90 degrees.
• Obtuse Triangle: A triangle with one angle greater than 90 degrees.
• Ordered Pair: (x, y) on a coordinate plane.
• Origin: (0,0) on a coordinate plane.
• Parallel Lines: Lines that never intersect.
• Parallelogram: A quadrilateral with parallel sides.
• Perimeter: Distance around a figure.
• Perpendicular Lines: Intersect to form right angles.
• Polygon: A closed figure with more than three sides.
• Pythagorean Theorem: a² + b² = c² for right triangles.
• Quadrilateral: A polygon with four sides.
• Radius: Half the diameter of a circle, from center to edge.
• Rectangle: A parallelogram with right angles.
• Regular Polygon: All sides and angles equal.
• Rhombus: A parallelogram with equal sides.
• Right Angle: Measures exactly 90 degrees.
• Right Triangle: Has a right angle.
• Scalene Triangle: No equal sides.
• Sector: A slice of a circle.
• Similar Polygons: Equal angles and proportional sides.
• Slope: Steepness of a line, (y₂-y₁)/(x₂-x₁).
• Square: A rectangle with equal sides.
• Supplementary Angles: Sum of 180 degrees.
• Surface Area: Sum of areas of a solid's faces.
• Tangent: Touches a circle at exactly one point.
• Transversal: Intersects two or more lines.
• Vertex: A point where lines meet.
• Volume: Number of cubic units inside a solid.

Important Formulas

Area and Volume

• Circle: A = πr²
• Rectangle: A = lw
• Triangle: A = ½bh
• Cylinder: V = πr²h
• Rectangle Solid: V = lwh

Angles

• Naming Angles: By vertex, a number, or three points.
• Measuring Angles: Notation m∠A.
• Classifying Angles:
  • Acute: < 90°
  • Right: = 90°
  • Obtuse: > 90° and < 180°
  • Straight: = 180°

Types of Triangles

• Scalene: No equal sides.
• Isosceles: Two equal sides.
• Equilateral: All sides equal.
• Acute: All angles < 90°.
• Right: One angle = 90°.
• Obtuse: One angle > 90°.

Pythagorean Theorem

• Used for calculating sides in right triangles, a² + b² = c².
• Pythagorean Triples: Common sets like (3, 4, 5).

Special Triangles

• 45-45-90 Triangle: Isosceles right triangles, hypotenuse = side√2.
• 30-60-90 Triangle: Different side ratios, hypotenuse = 2 × short leg.

Circle Geometry

• Central Angles and Arcs: Arc length = (central angle/360) × 2πr.

Coordinate Geometry

• Graphing Points: Using (x, y) coordinates.
• Distance Formula: d = √((x₂-x₁)² + (y₂-y₁)²).
• Midpoint Formula: Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).
• Slope: (y₂-y₁) / (x₂-x₁).

Quadrilaterals and Polygons

• Sum of Interior Angles: (n-2) × 180° for n-sided polygon.
• Sum of Exterior Angles: Always 360°.
• Parallelogram Properties: Opposite sides and angles are equal, diagonals bisect each other.

Solid Figures

• Perimeter: Sum of all sides.
• Area: Square units within a figure.
• Volume: Cubic units within a solid.

Practice Questions

• The document includes various practice questions and answers to test understanding of these topics.