Math Chapter 12: Midpoint Theorem and Geometry
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Questions and Answers

What is the main conclusion of the midpoint theorem in a triangle?

  • The angle at the midpoint of a triangle's side measures 90 degrees.
  • The line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. (correct)
  • The perpendicular drawn from the vertex of a triangle to the opposite side bisects the side.
  • The line segment bisecting the angle of a triangle is perpendicular to the opposite side.
  • According to the Pythagorean theorem, what is the relationship between the sides of a right triangle?

  • The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (correct)
  • The product of the lengths of the legs is equal to the area of the right triangle.
  • The sum of the lengths of the legs is equal to the length of the hypotenuse.
  • The ratio of the hypotenuse to the opposite side is equal to the sine of the angle.
  • In the context of arcs in circles, what is an inscribed angle?

  • An angle formed by two radii of the circle.
  • An angle whose vertex is on the circumference of the circle and is equal to 90 degrees.
  • An angle whose vertex is on the circle and whose sides contain chords of the circle. (correct)
  • An angle whose vertex is at the center of the circle.
  • Which of the following statements about rational fractions is correct?

    <p>A rational fraction is the ratio of two polynomials.</p> Signup and view all the answers

    Which equation is an example of a remarkable identity?

    <p>$(a+b)^2 = a^2 + 2ab + b^2$</p> Signup and view all the answers

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