Gr12 Mathematics: Ch 7.3 Triangles
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Questions and Answers

What is the conclusion of triangles with the same height?

  • Triangles with equal heights have areas proportional to their heights.
  • Triangles with equal heights have bases proportional to their areas.
  • Triangles with equal heights have areas equal to each other.
  • Triangles with equal heights have areas proportional to their bases. (correct)

    • What is the formula to find the area of triangle ABC?

  • Area = BC * h
  • Area = (1/3) * BC * h
  • Area = BC / h
  • Area = (1/2) * BC * h (correct)

    • What can be concluded about two triangles on the same base and equal in area?

  • The triangles are congruent.
  • The triangles lie between parallel lines. (correct)
  • The triangles have equal heights.
  • The triangles have equal perimeters.

    • What is the statement of the Proportion Theorem?

    <p>A line drawn parallel to one side of a triangle divides the other two sides of the triangle in the same proportion.</p> Signup and view all the answers

    What is the formula of the Proportion Theorem?

    <p>AD/DB = AE/EC</p> Signup and view all the answers

    What is the statement of the Mid-point Theorem?

    <p>The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side.</p> Signup and view all the answers

    What can be concluded about triangles with the same base and between the same parallel lines?

    <p>The triangles have equal areas.</p> Signup and view all the answers

    What is the purpose of drawing perpendiculars in the proof of the Proportion Theorem?

    <p>To show that the line divides the sides proportionally.</p> Signup and view all the answers

    What is the condition for the Mid-point Theorem to be applied?

    <p>If the line joining the midpoints of two sides of a triangle is parallel to the third side</p> Signup and view all the answers

    What is the formula to find the area of a triangle?

    <p>Area = (1/2) × base × height</p> Signup and view all the answers

    What can be said about the areas of two triangles with equal heights?

    <p>They are proportional to their bases</p> Signup and view all the answers

    What is the condition for two triangles to be similar?

    <p>If they are equiangular</p> Signup and view all the answers

    What is the Proportion Theorem?

    <p>A line drawn parallel to one side of a triangle divides the other two sides proportionally</p> Signup and view all the answers

    What is the converse of the Mid-point Theorem?

    <p>The line drawn from the midpoint of one side of a triangle parallel to another side bisects the third side of the triangle</p> Signup and view all the answers

    If DE is parallel to BC and AD = 4, what is the length of DB?

    <p>6</p> Signup and view all the answers

    In a triangle, if the line joining the midpoints of two sides is drawn, what can be said about the line?

    <p>It is parallel to the third side and half its length.</p> Signup and view all the answers

    What is the ratio of the areas of two triangles with equal heights?

    <p>Directly proportional to the bases</p> Signup and view all the answers

    If two triangles are equiangular, what can be said about the corresponding sides?

    <p>They are proportional</p> Signup and view all the answers

    What is the converse of the Mid-point Theorem?

    <p>The line drawn from the midpoint of one side of a triangle bisects the third side.</p> Signup and view all the answers

    If two triangles have proportional corresponding sides, what can be said about the triangles?

    <p>They are similar</p> Signup and view all the answers

    What can be said about the heights of two triangles on the same base and equal in area?

    <p>They are equal.</p> Signup and view all the answers

    If a line is drawn parallel to one side of a triangle, what can be said about the other two sides?

    <p>They are divided in the same ratio.</p> Signup and view all the answers

    What is the ratio of the areas of two triangles with equal heights and bases in the ratio of 2:3?

    <p>2:3</p> Signup and view all the answers

    If two triangles have areas in the ratio of 2:3 and their heights are equal, what can be said about their bases?

    <p>Their bases are in the ratio of 2:3.</p> Signup and view all the answers

    What is the length of the line joining the midpoints of two sides of a triangle?

    <p>Half the length of the third side.</p> Signup and view all the answers

    What can be said about the areas of two triangles with the same base and between the same parallel lines?

    <p>They are equal.</p> Signup and view all the answers

    If two triangles have equal areas and their bases are in the ratio of 2:3, what can be said about their heights?

    <p>Their heights are in the ratio of 3:2.</p> Signup and view all the answers

    What is the purpose of drawing perpendiculars in the proof of the Proportion Theorem?

    <p>To show that the line divides the sides proportionally.</p> Signup and view all the answers

    What can be concluded about two triangles with proportional areas and equal heights?

    <p>They have proportional bases.</p> Signup and view all the answers

    In the proof of the Proportion Theorem, why are perpendiculars drawn from E to AD and from D to AE?

    <p>To show that the line divides the sides proportionally.</p> Signup and view all the answers

    If two triangles have equal areas and their bases are in the ratio of 2:3, what can be said about their heights?

    <p>Their heights are in the ratio of 3:2.</p> Signup and view all the answers

    What is the condition for two triangles to have areas in a certain ratio?

    <p>They should have proportional corresponding sides.</p> Signup and view all the answers

    What can be concluded about a line drawn parallel to one side of a triangle?

    <p>It divides the other two sides in the same proportion.</p> Signup and view all the answers

    If two triangles have proportional corresponding sides, what can be said about their areas?

    <p>They are in a certain ratio.</p> Signup and view all the answers

    What is the ratio of the areas of two triangles with equal heights and bases in the ratio of 2:3?

    <p>2:3</p> Signup and view all the answers

    What can be said about the heights of two triangles on the same base and equal in area?

    <p>They are equal.</p> Signup and view all the answers

    If two triangles have proportional corresponding sides and one of them has a side of length 6 units, what can be said about the corresponding side in the other triangle?

    <p>It is greater than 6 units</p> Signup and view all the answers

    If a line is drawn parallel to one side of a triangle and intersects the other two sides, what can be said about the line segments formed?

    <p>They are proportional to the original sides</p> Signup and view all the answers

    If two triangles have equal areas and their heights are in the ratio of 2:3, what can be said about their bases?

    <p>They are in the ratio of 3:2</p> Signup and view all the answers

    If a line is drawn through the midpoint of one side of a triangle, what can be said about the line and the third side of the triangle?

    <p>The line is parallel to the third side and half its length</p> Signup and view all the answers

    If two triangles have bases in the ratio of 2:3 and their areas are equal, what can be said about their heights?

    <p>They are equal</p> Signup and view all the answers

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