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Geometry Chapters 6-11 Flashcards
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Geometry Chapters 6-11 Flashcards

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Questions and Answers

What is Chapter 6?

Geometry content.

Two polygons are similar if:

  • Corresponding sides are congruent (correct)
  • Corresponding angles are equal
  • Corresponding sides are equal
  • Corresponding angles are congruent (correct)
  • What is reflection in geometry?

    Creates a mirror image by reflecting a figure over something.

    What is rotation?

    <p>Turns a figure about a set point.</p> Signup and view all the answers

    What is translation?

    <p>Slides in any direction.</p> Signup and view all the answers

    Which are ways to prove triangles similar?

    <p>AA (Angle-Angle)</p> Signup and view all the answers

    What is the 45-45-90 theorem?

    <p>Triangle properties for equal legs and hypotenuse.</p> Signup and view all the answers

    What is the 30-60-90 theorem?

    <p>Hypotenuse = 2 * shorter leg; longer leg = shorter leg * √3.</p> Signup and view all the answers

    When do you use inverse trigonometry (sin-1)?

    <p>To find an angle measure.</p> Signup and view all the answers

    What are the interior angles of a quadrilateral?

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

    How do you find the angle sum in a polygon?

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

    What does the Polygon Exterior Angles Theorem state?

    <p>Exterior angles will add up to 360 degrees.</p> Signup and view all the answers

    What is a parallelogram?

    <p>A quadrilateral with both pairs of opposite sides parallel.</p> Signup and view all the answers

    What is a rhombus?

    <p>Parallelogram with four congruent sides and perpendicular diagonals.</p> Signup and view all the answers

    What is a rectangle?

    <p>Parallelogram with four right angles.</p> Signup and view all the answers

    What is a square?

    <p>Parallelogram with four right angles and four congruent sides.</p> Signup and view all the answers

    What is a trapezoid?

    <p>A quadrilateral with exactly one pair of parallel sides.</p> Signup and view all the answers

    When is a trapezoid considered isosceles?

    <p>If each pair of base angles is congruent and diagonals are congruent.</p> Signup and view all the answers

    What is the midsegment on a trapezoid?

    <p>1/2 length of bases combined.</p> Signup and view all the answers

    What are tangent circles?

    <p>Circles that touch at exactly one point.</p> Signup and view all the answers

    What are concentric circles?

    <p>Circles that have the same center but different radii.</p> Signup and view all the answers

    What is the standard equation of a circle?

    <p>(x-h)² + (y-k)² = r².</p> Signup and view all the answers

    How can you describe a translation?

    <p>(x,y) --&gt; (x+a, y+b).</p> Signup and view all the answers

    What is the component form of a vector?

    <p>Horizontal then vertical.</p> Signup and view all the answers

    What is the reflection in the x-axis?

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

    What is the reflection in the y-axis?

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

    What is the result of reflecting a point in the line y=x?

    <p>(b,a).</p> Signup and view all the answers

    How is a point reflected in the line y=-x?

    <p>(-b, -a).</p> Signup and view all the answers

    What are the coordinates after rotating a point 90 degrees?

    <p>(-b, a).</p> Signup and view all the answers

    What happens when you rotate a point 180 degrees?

    <p>(-a, -b).</p> Signup and view all the answers

    What happens when you rotate a point 270 degrees?

    <p>(b, -a).</p> Signup and view all the answers

    What does the Reflections in Intersecting Lines Theorem state?

    <p>The angle of rotation is 2x.</p> Signup and view all the answers

    What is the circumference of a circle?

    <p>2πr or πd.</p> Signup and view all the answers

    What is the formula for arc length?

    <p>Length/2Ï€r = Measure/360.</p> Signup and view all the answers

    What is the area of a circle?

    <p>πr².</p> Signup and view all the answers

    What is the area of a sector?

    <p>Area/πr² = Measure/360.</p> Signup and view all the answers

    How do you calculate the probability a point is on an area of a line?

    <p>Length of smaller/Length of larger.</p> Signup and view all the answers

    What is the area of a right cone?

    <p>πr² + πrl.</p> Signup and view all the answers

    What is the area of a cylinder?

    <p>2πr² + 2πrh.</p> Signup and view all the answers

    What is the area of a sphere?

    <p>4πr².</p> Signup and view all the answers

    What is the area of a trapezoid?

    <p>1/2h(b1+b2).</p> Signup and view all the answers

    What is the volume of a cylinder?

    <p>πr²h.</p> Signup and view all the answers

    What is the volume of a solid?

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

    What is the volume of a cone?

    <p>1/3πr²h.</p> Signup and view all the answers

    What is the volume of a pyramid?

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

    What is the volume of a sphere?

    <p>4/3πr³.</p> Signup and view all the answers

    What does Euler's Theorem state?

    <p>V + F = E + 2.</p> Signup and view all the answers

    What is a chord?

    <p>A segment whose endpoints are on the circle.</p> Signup and view all the answers

    What is a secant?

    <p>A line that intersects a circle in two points.</p> Signup and view all the answers

    What is a tangent?

    <p>Intersects the circle at exactly one point.</p> Signup and view all the answers

    What is a central angle?

    <p>An angle whose vertex is the center of the circle.</p> Signup and view all the answers

    What is the difference between minor arc and major arc?

    <p>Minor arc is shorter than the circle, major arc is longer.</p> Signup and view all the answers

    What are adjacent arcs?

    <p>Two arcs of the same circle that intersect at one point.</p> Signup and view all the answers

    What is an inscribed angle?

    <p>Angle whose vertex is on the circle and contains chords of the circle.</p> Signup and view all the answers

    Study Notes

    Chapter 6: Basic Transformations and Similarity

    • Similar polygons have congruent corresponding angles and proportional corresponding sides.
    • Reflection creates a mirror image across a line or axis.
    • Rotation involves turning a figure around a specific point.
    • Translation refers to sliding a figure in any direction without altering its shape.

    Chapter 7: Triangle Similarity

    • Triangles can be proven similar using:
      • AA (Angle-Angle) postulate
      • SSS (Side-Side-Side) similarity
      • SAS (Side-Angle-Side) similarity.
    • The 45-45-90 theorem relates the lengths of the legs to the hypotenuse: hypotenuse = leg * √2.
    • In a 30-60-90 triangle, the relationships are:
      • Hypotenuse = 2 × shorter leg
      • Longer leg = shorter leg × √3.

    Chapter 8: Angles in Polygons

    • The sum of interior angles in a quadrilateral is 360 degrees.
    • To find the angle sum of any polygon, use the formula: (sides - 2) * 180.
    • According to the Polygon Exterior Angles Theorem, the sum of exterior angles of any polygon equals 360 degrees.

    Quadrilaterals Characteristics

    • A parallelogram has opposite sides that are equal and parallel, with bisecting diagonals and congruent opposite angles.
    • A rhombus is a type of parallelogram with four equal sides and perpendicular diagonals.
    • A rectangle is a parallelogram with four right angles.
    • A square is a special parallelogram that has both four right angles and four congruent sides.
    • A trapezoid features one pair of parallel sides known as bases.
    • An isosceles trapezoid has congruent base angles and equal diagonals.

    Chapter 9 and 10: Circles and their Properties

    • Tangent circles touch at exactly one point.
    • Concentric circles share the same center but have different radii.
    • The standard equation of a circle with center (h, k) and radius r is given by: (x - h)² + (y - k)² = r².

    Transformations and Vectors

    • A translation can be described by the notation: (x,y) → (x+a, y+b).
    • The component form of a vector consists of its horizontal and vertical movements.
    • Reflection in the x-axis transforms a point (x, y) to (x, -y).
    • Reflection in the y-axis transforms a point (x, y) to (-x, y).
    • Reflection in the line y = x changes a point (b, a) to (b, a).
    • Rotation transformations involve:
      • 90 degrees: (-b, a)
      • 180 degrees: (-a, -b)
      • 270 degrees: (b, -a).

    Chapter 11: Measurement of Circles and Solids

    • The circumference of a circle can be calculated using either 2Ï€r or Ï€d.
    • Arc length determination uses the ratio: Length/2Ï€r = Measure/360.
    • The area of a circle can be found using the formula: Ï€r².
    • The area of a sector of a circle follows: Area/Ï€r² = Measure/360.

    Areas and Volumes of Solids

    • The area of a right cone includes the base area (Ï€r²) plus the lateral area (Ï€rl).
    • The area of a cylinder combines the base areas and lateral surface area: 2Ï€r² + 2Ï€rh.
    • The surface area of a sphere is calculated as 4Ï€r².
    • The area of a trapezoid is given by: 1/2h(b1+b2).
    • Volume calculations are characterized by:
      • Cylinder: Ï€r²h
      • Cone: 1/3Ï€r²h
      • Pyramid: 1/3Bh
      • Sphere: 4/3Ï€r³.

    Euler's Theorem and Circle Terminology

    • Euler's Theorem states the relation: V + F = E + 2, where V is vertices, F is faces, and E is edges.
    • A chord is a segment with endpoints on the circle.
    • A secant is a line that intersects a circle at two points.
    • A tangent touches a circle at exactly one point.
    • A central angle has its vertex at the circle's center.
    • Minor and major arcs are segments of a circle, defined by their angles.
    • Adjacent arcs are arcs that intersect at a single point.
    • An inscribed angle is formed by two chords from the circle.

    Coordinate Geometry

    • The distance formula calculates the distance between two points in the coordinate plane.
    • The midpoint formula determines the midpoint between two endpoints on a line segment.
    • The slope is defined as the ratio of the rise over the run between two points on a line.

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    Test your knowledge on key concepts from Geometry Chapters 6-11 with these flashcards. Each card focuses on important definitions and principles, including similarity of polygons, geometric transformations like reflection, rotation, and translation. Perfect for quick reviews or study sessions!

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