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Questions and Answers
What is the longest possible chord in a circle?
What is the longest possible chord in a circle?
What is the formula for the sine of an angle in a right triangle?
What is the formula for the sine of an angle in a right triangle?
What is the criterion for similarity of triangles?
What is the criterion for similarity of triangles?
What is the sum of the measures of complementary angles?
What is the sum of the measures of complementary angles?
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What is the intersection of two planes?
What is the intersection of two planes?
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What is the center of a circle?
What is the center of a circle?
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What is the formula for the cosine of an angle in a right triangle?
What is the formula for the cosine of an angle in a right triangle?
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What is the criterion for congruence of triangles?
What is the criterion for congruence of triangles?
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What is the measure of a straight angle?
What is the measure of a straight angle?
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What is a point in geometry?
What is a point in geometry?
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Study Notes
Geometry EOC Prep
Circles and Circle Theorems
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Circle properties:
- Center: midpoint of a diameter
- Radius: distance from center to any point on the circle
- Diameter: longest possible chord, passes through center
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Circle theorems:
- Inscribed angle theorem: angle at the center of a circle is twice the inscribed angle
- Central angle theorem: angle at the center of a circle is equal to the sum of the inscribed angles
- Intercepted arc theorem: the angle at the center of a circle is equal to the sum of the intercepted arcs
Right Triangles and Trigonometry
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Right triangle properties:
- Hypotenuse: longest side, opposite the right angle
- Legs: sides that meet at the right angle
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Trigonometric ratios:
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
- Pythagorean identity: sin^2(A) + cos^2(A) = 1
Properties of Congruent and Similar Figures
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Congruent figures:
- Same shape and size
- Corresponding angles and sides are equal
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Similar figures:
- Same shape, different size
- Corresponding angles are equal, corresponding sides are proportional
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Criteria for congruence and similarity:
- SAS (side-angle-side), ASA (angle-side-angle), SSS (side-side-side) for congruence
- AA (angle-angle) for similarity
Angles and Measurement
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Angle properties:
- Complementary angles: add up to 90°
- Supplementary angles: add up to 180°
- Vertical angles: formed by two intersecting lines
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Angle measurement:
- Degrees: 360° in a circle, 180° in a straight angle
- Radians: 2π in a circle, π in a straight angle
Points, Lines, and Planes
- Point: location in space, represented by an ordered pair (x, y)
- Line: set of points extending infinitely in two directions
- Plane: set of points extending infinitely in all directions
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Intersections:
- Two lines intersect at a point
- A line and a plane intersect at a line
- Two planes intersect at a line
Volume and Surface Area of 3D Shapes
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Volume:
- Rectangular prism: V = lwh
- Cylinder: V = πr^2h
- Cone: V = (1/3)πr^2h
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Surface area:
- Rectangular prism: SA = 2(lw + lh + wh)
- Cylinder: SA = 2πr(h + r)
- Cone: SA = πr(r + l)
Weighted Average
- Weighted average formula: (Σ(xi * wi)) / Σwi
- xi: individual data points
- wi: weights assigned to each data point
Transformations, Rotations, and Dilatations
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Transformations:
- Translation: movement in a straight line
- Reflection: flip over a line
- Rotation: turn around a fixed point
-
Rotations:
- Center of rotation: fixed point around which the rotation occurs
- Angle of rotation: measure of the rotation
-
Dilatations:
- Scale factor: multiplier applied to each dimension
- Center of dilation: fixed point around which the dilation occurs
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Description
Prepare for your Geometry End-of-Course exam with this comprehensive review of key concepts, including circles, right triangles, congruent and similar figures, angles, and 3D shapes.
