Geometry EOC Review Flashcards
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Questions and Answers

How do you go from short leg to hypotenuse in a 45-45-90 triangle?

  • x times 2
  • x times radical 3
  • x times 4
  • x times radical 2 (correct)

    • How do you go from short leg to long leg in a 30-60-90 triangle?

  • x times 2
  • x times radical 2
  • x times radical 3 (correct)
  • x times 4

    • How do you go from short leg to hypotenuse in a 30-60-90 triangle?

  • x times radical 2
  • x times radical 3
  • x times 2 (correct)
  • x times 4

    • 90 degrees clockwise/270 degrees counterclockwise rotation: (x, y) -> (____, ____)?

    <p>(y, -x)</p> Signup and view all the answers

    180 degrees rotation: (x, y) -> (____, ____)?

    <p>(-x, -y)</p> Signup and view all the answers

    270 degrees clockwise/90 degrees counterclockwise rotation: (x, y) -> (____, ____)?

    <p>(-y, x)</p> Signup and view all the answers

    Reflection across the x-axis: (x, y) -> (____, ____)?

    <p>(x, -y)</p> Signup and view all the answers

    Reflection across the y-axis: (x, y) -> (____, ____)?

    <p>(-x, y)</p> Signup and view all the answers

    Reflection across the line y=x: (x, y) -> (____, ____)?

    <p>(y, x)</p> Signup and view all the answers

    What does SOH in SOHCAHTOA represent?

    <p>sin = opp/hyp</p> Signup and view all the answers

    What does CAH in SOHCAHTOA represent?

    <p>cos = adj/hyp</p> Signup and view all the answers

    What does TOA in SOHCAHTOA represent?

    <p>tan = opp/adj</p> Signup and view all the answers

    What is the formula for the surface area of a sphere?

    <p>4pi(r)squared</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>4/3pi(r)cubed</p> Signup and view all the answers

    What is the formula for the volume of a prism or cylinder?

    <p>Bh</p> Signup and view all the answers

    What is the formula for the volume of a pyramid or cone?

    <p>1/3Bh</p> Signup and view all the answers

    What is the Pythagorean theorem?

    <p>c(squared) = a(squared) + b(squared)</p> Signup and view all the answers

    What are Pythagorean triples?

    <p>(3,4,5), (5,12,13), (7,24,25)</p> Signup and view all the answers

    How do you find arc length?

    <p>x/360 times 2pi(r)</p> Signup and view all the answers

    How do you find the area of a sector?

    <p>x/360 times pi(r)squared</p> Signup and view all the answers

    What is the standard equation of a circle?

    <p>(x-h)squared + (y-k)squared = (r)squared</p> Signup and view all the answers

    What is the Law of Detachment?

    <p>If p-&gt;q and p is true, then q is true</p> Signup and view all the answers

    What is a conditional statement?

    <p>if p, then q</p> Signup and view all the answers

    What is a converse?

    <p>if q, then p</p> Signup and view all the answers

    What is the inverse?

    <p>if not p, then not q</p> Signup and view all the answers

    What is the contrapositive?

    <p>if not q, then not p</p> Signup and view all the answers

    What is a biconditional statement?

    <p>p if and only if q</p> Signup and view all the answers

    What is the Law of Syllogism?

    <p>if p-&gt;q and q-&gt;r, then p-&gt;r</p> Signup and view all the answers

    What is the formula for slope?

    <p>rise/run</p> Signup and view all the answers

    Parallel lines have the ______ slope.

    <p>same</p> Signup and view all the answers

    Two perpendicular lines have _______ slopes and they are _______.

    <p>opposite, reciprocals</p> Signup and view all the answers

    What is a scale factor?

    <p>a:b</p> Signup and view all the answers

    What is the ratio of perimeters?

    <p>a:b</p> Signup and view all the answers

    What is the ratio of areas?

    <p>a(squared):b(squared)</p> Signup and view all the answers

    What is the ratio of volumes?

    <p>a(cubed):b(cubed)</p> Signup and view all the answers

    What is the formula for the interior angles sum of a polygon?

    <p>(n-2)*180</p> Signup and view all the answers

    What is the formula for each interior angle of a regular polygon?

    <p>(n-2)(180)/n</p> Signup and view all the answers

    What is the sum of the exterior angles of a polygon?

    <p>360 degrees</p> Signup and view all the answers

    What is the formula for each exterior angle of a regular polygon?

    <p>360/n</p> Signup and view all the answers

    Study Notes

    Triangle Measurements

    • In a 45-45-90 triangle, the hypotenuse is calculated as x times √2 from the short leg.
    • In a 30-60-90 triangle, the long leg is x times √3, while the hypotenuse is x times 2 from the short leg.

    Rotation Transformations

    • A point (x, y) rotates 90 degrees clockwise or 270 degrees counterclockwise to (y, -x).
    • A 180-degree rotation transforms (x, y) to (-x, -y).
    • A 270-degree clockwise or 90 degrees counterclockwise rotation changes (x, y) to (-y, x).

    Reflection Transformations

    • Reflection across the x-axis results in (x, -y).
    • Reflection across the y-axis changes (x, y) to (-x, y).
    • Reflection across the line y = x transforms (x, y) to (y, x).

    Trigonometric Ratios

    • Sine function: sin = opposite/hypotenuse (SOH).
    • Cosine function: cos = adjacent/hypotenuse (CAH).
    • Tangent function: tan = opposite/adjacent (TOA).

    Surface Area and Volume Formulas

    • Surface area of a sphere is calculated as 4πr².
    • Volume of a sphere is 4/3πr³, similarly applies to cubes.
    • Volume of a prism or cylinder is given by the formula B*h, where B is the base area.
    • Volume of a pyramid or cone is calculated as (1/3)Bh.

    Pythagorean Theorem and Triples

    • Pythagorean theorem states c² = a² + b².
    • Common Pythagorean triples include (3, 4, 5), (5, 12, 13), and (7, 24, 25).

    Arc Length and Sector Area

    • Arc length can be found using the formula (x/360) * 2πr.
    • Area of a sector is calculated as (x/360) * πr².

    Circle Equation

    • The standard equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center and r is the radius.

    Logic Statements

    • Law of Detachment: If p implies q and p is true, then q must be true.
    • A conditional statement is expressed as "if p, then q."
    • The converse states "if q, then p."
    • The inverse states "if not p, then not q."
    • The contrapositive states "if not q, then not p."
    • A biconditional is stated as "p if and only if q."
    • Law of Syllogism states if p implies q and q implies r, then p implies r.

    Slope and Parallelism

    • Slope formula is given by rise/run.
    • Parallel lines have identical (same) slopes.
    • Perpendicular lines have slopes that are opposites and reciprocals of each other.

    Scale Factors and Ratios

    • Scale factor is expressed as a:b.
    • The ratio of perimeters is also a:b.
    • The ratio of areas is represented as a²:b².
    • The ratio of volumes is expressed as a³:b³.

    Angles in Polygons

    • The sum of interior angles in an n-sided polygon is (n-2) * 180 degrees.
    • Each interior angle of a regular n-sided polygon is (n-2)(180)/n.
    • The sum of exterior angles for any polygon is always 360 degrees.
    • Each exterior angle of a regular n-sided polygon is calculated as 360/n.

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    Prepare for your Geometry End-of-Course exam with these review flashcards. Each card covers key concepts such as triangle properties and rotations. Test your knowledge on 45-45-90 and 30-60-90 triangles.

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