24 Questions
What is the characteristic of perpendicular lines?
They form right angles with each other
How do you construct a perpendicular line through a point not on the line segment?
Draw two circles with the end points of the line segment as the centers and passing through the given point
What is the purpose of drawing two equal circles in constructing a perpendicular line at a point on the line segment?
To find the points where the first circle intersects the line segment
How do you bisect an angle using circles?
Draw a circle with the vertex of the angle as the center and mark off equal lengths on both arms of the angle
What is the first step in constructing a 45° angle?
Draw a 90° angle using the method for constructing perpendicular lines
What is the result of constructing two equal circles where each circle passes through the center of the other?
An equilateral triangle with 60° angles
What is the characteristic of the triangle formed by constructing two equal circles where each circle passes through the center of the other?
An equilateral triangle with three 60° angles
What is the purpose of labeling the centers of the circles and the points of intersection in constructing 60° and 30° angles?
To form an equilateral triangle
What is the significance of the 90-degree angle in constructing perpendicular lines?
It forms a right angle with the given line segment.
In Case 1 of constructing a perpendicular line, what is the center of the first circle?
One end point of the line segment
What is the purpose of drawing two equal circles in Case 2 of constructing a perpendicular line?
To find the points where the first circle intersects the line segment
What is the result of bisecting a 90° angle?
A 45° angle
What is the shape formed by constructing two equal circles where each circle passes through the center of the other?
An equilateral triangle
What is the angle measure at each vertex of the equilateral triangle formed in constructing 60° and 30° angles?
60°
What is the purpose of drawing a circle with the vertex of the angle as the center in bisecting an angle?
To mark off equal lengths on both arms of the angle
What is the result of bisecting a 60° angle?
A 30° angle
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?
To intersect with the given point
What is the common feature of the circles used in Case 2 of constructing a perpendicular line?
They have equal radii
What is the result of using the method of bisecting an angle to construct a 45° angle?
A 45° angle is formed
What is the shape formed by the line segments in constructing 60° and 30° angles?
An equilateral triangle
What is the purpose of drawing a line from the vertex through the points where the two circles intersect in bisecting an angle?
To bisect the angle
What is the condition for the circles drawn in Case 1 of constructing a perpendicular line?
They have equal radii
What is the common feature of the points where the circles intersect in Case 2 of constructing a perpendicular line?
They are equidistant from the line segment
What is the result of constructing two equal circles where each circle passes through the center of the other?
An equilateral triangle is formed
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