Comprehensive ACT Geometry Review: Plane, Coordinate, and Trigonometry
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Multiple Choice
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30 Terms
Vertical Angles
Angles opposite each other when two lines intersect; always congruent.
Supplementary Angles
Two angles that add up to 180°.
Complementary Angles
Two angles that add up to 90°.
Transversal
A line that cuts across two parallel lines.
Alternate Interior Angles
Equal angles formed when a transversal crosses parallel lines.
Corresponding Angles
Equal angles in matching corners when a transversal crosses parallel lines.
Consecutive Interior Angles
Angles that sum to 180° formed by a transversal crossing parallel lines.
Interior Angle Sum Formula
For any polygon with n sides, the sum is (n-2) × 180°.
Exterior Angles of a Polygon
The sum is always 360° for any convex polygon.
Congruent Figures
Figures that have the exact same shape and size.
Similarity in Geometry
Figures that have the same shape but different sizes.
AA Criterion
Two triangles are similar if they share two angle measures.
Ratio of Areas in Similar Figures
If the ratio of side lengths is k, the ratio of areas is k².
Triangle Sum Theorem
The sum of interior angles in any triangle is always 180°.
Triangle Inequality Theorem
The sum of any two sides must be greater than the length of the third side.
Pythagorean Theorem
For right triangles, a² + b² = c².
Common Pythagorean Triples
3-4-5, 5-12-13, 8-15-17, and 7-24-25.
Special Right Triangle Ratios
45-45-90: x : x : x√2; 30-60-90: x : x√3 : 2x.
SOH CAH TOA
Mnemonic for sine, cosine, and tangent ratios.
Sine Function
sin(θ) = Opposite/Hypotenuse.
Cosine Function
cos(θ) = Adjacent/Hypotenuse.
Tangent Function
tan(θ) = Opposite/Adjacent.
Circumference of a Circle
C = 2πr or C = πd.
Area of a Circle
A = πr².
Arc Length Formula
Arc Length = (n/360) × 2πr.
Sector Area Formula
Sector Area = (n/360) × πr².
Circle Equation
Standard form: (x - h)² + (y - k)² = r².
Slope-Intercept Form
y = mx + b, where m is the slope.
Distance Formula
d = √((x2 - x1)² + (y2 - y1)²).
Midpoint Formula
Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
