Gr 9 MATH: Ch 9.2 Constructions
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Questions and Answers

What is the characteristic of perpendicular lines?

  • They are parallel to each other
  • They form right angles with each other (correct)
  • They intersect at a 45-degree angle
  • They never intersect

    • How do you construct a perpendicular line through a point not on the line segment?

  • Draw a circle with the given point as the center and passing through the line segment
  • Draw two circles with the end points of the line segment as the centers and passing through the given point (correct)
  • Draw a circle with the midpoint of the line segment as the center and passing through the given point
  • Draw a circle with the given point as the center and passing through the midpoint of the line segment

    • What is the purpose of drawing two equal circles in constructing a perpendicular line at a point on the line segment?

  • To draw a parallel line
  • To find the points where the first circle intersects the line segment (correct)
  • To find the midpoint of the line segment
  • To bisect the angle

    • How do you bisect an angle using circles?

    <p>Draw a circle with the vertex of the angle as the center and mark off equal lengths on both arms of the angle</p> Signup and view all the answers

    What is the first step in constructing a 45° angle?

    <p>Draw a 90° angle using the method for constructing perpendicular lines</p> Signup and view all the answers

    What is the result of constructing two equal circles where each circle passes through the center of the other?

    <p>An equilateral triangle with 60° angles</p> Signup and view all the answers

    What is the characteristic of the triangle formed by constructing two equal circles where each circle passes through the center of the other?

    <p>An equilateral triangle with three 60° angles</p> Signup and view all the answers

    What is the purpose of labeling the centers of the circles and the points of intersection in constructing 60° and 30° angles?

    <p>To form an equilateral triangle</p> Signup and view all the answers

    What is the significance of the 90-degree angle in constructing perpendicular lines?

    <p>It forms a right angle with the given line segment.</p> Signup and view all the answers

    In Case 1 of constructing a perpendicular line, what is the center of the first circle?

    <p>One end point of the line segment</p> Signup and view all the answers

    What is the purpose of drawing two equal circles in Case 2 of constructing a perpendicular line?

    <p>To find the points where the first circle intersects the line segment</p> Signup and view all the answers

    What is the result of bisecting a 90° angle?

    <p>A 45° angle</p> Signup and view all the answers

    What is the shape formed by constructing two equal circles where each circle passes through the center of the other?

    <p>An equilateral triangle</p> Signup and view all the answers

    What is the angle measure at each vertex of the equilateral triangle formed in constructing 60° and 30° angles?

    <p>60°</p> Signup and view all the answers

    What is the purpose of drawing a circle with the vertex of the angle as the center in bisecting an angle?

    <p>To mark off equal lengths on both arms of the angle</p> Signup and view all the answers

    What is the result of bisecting a 60° angle?

    <p>A 30° angle</p> Signup and view all the answers

    What is the purpose of drawing a circle with one end point of the line segment as the center in Case 1 of constructing a perpendicular line?

    <p>To intersect with the given point</p> Signup and view all the answers

    What is the common feature of the circles used in Case 2 of constructing a perpendicular line?

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

    What is the result of using the method of bisecting an angle to construct a 45° angle?

    <p>A 45° angle is formed</p> Signup and view all the answers

    What is the shape formed by the line segments in constructing 60° and 30° angles?

    <p>An equilateral triangle</p> Signup and view all the answers

    What is the purpose of drawing a line from the vertex through the points where the two circles intersect in bisecting an angle?

    <p>To bisect the angle</p> Signup and view all the answers

    What is the condition for the circles drawn in Case 1 of constructing a perpendicular line?

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

    What is the common feature of the points where the circles intersect in Case 2 of constructing a perpendicular line?

    <p>They are equidistant from the line segment</p> Signup and view all the answers

    What is the result of constructing two equal circles where each circle passes through the center of the other?

    <p>An equilateral triangle is formed</p> Signup and view all the answers

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