Geometry Geometry Constructions & Loci 1 — Questions and Answers
Question 1: Which tools are traditionally used in geometric constructions?
- Ruler and protractor
- Compass and straightedge (Correct answer)
- Calculator and ruler
- Graph paper and pencil
Correct answer: Compass and straightedge
Classical geometric constructions use only a compass and a straightedge (unmarked ruler).
Question 2: What is the locus of all points equidistant from two fixed points A and B?
- A circle passing through A and B
- The line segment AB
- The perpendicular bisector of AB (Correct answer)
- A parabola
Correct answer: The perpendicular bisector of AB
The set of all points equidistant from two fixed points is the perpendicular bisector of the segment joining them.
Question 3: To bisect an angle using a compass and straightedge, what is the first step?
- Draw a line parallel to one ray
- Place the compass point at the vertex and draw an arc intersecting both rays (Correct answer)
- Measure the angle with a protractor and divide by 2
- Draw a perpendicular line from the vertex
Correct answer: Place the compass point at the vertex and draw an arc intersecting both rays
The first step is to place the compass at the vertex and draw an arc that intersects both rays of the angle.
Question 4: What is the locus of all points equidistant from a fixed point (center)?
- A straight line
- A parabola
- A circle (Correct answer)
- An ellipse
Correct answer: A circle
The locus of all points at a fixed distance from a center point is a circle.
Question 5: How do you construct the perpendicular bisector of a line segment?
- Draw arcs from each endpoint with equal radii greater than half the segment's length, then connect the intersection points (Correct answer)
- Measure the segment and mark the midpoint, then draw a line through it
- Use a protractor to measure 90° at the midpoint
- Draw a line parallel to the segment
Correct answer: Draw arcs from each endpoint with equal radii greater than half the segment's length, then connect the intersection points
Open the compass to more than half the segment's length, draw intersecting arcs from both endpoints, and connect the two intersection points.
Question 6: What does it mean to 'construct' a geometric figure?
- To draw it freehand as accurately as possible
- To create it using only a compass and straightedge following defined rules (Correct answer)
- To measure and draw it using a ruler and protractor
- To model it in a 3D program
Correct answer: To create it using only a compass and straightedge following defined rules
A geometric construction uses only a compass and straightedge (no measurements), following classical rules.
Geometry Geometry Constructions & Loci 1
Which tools are traditionally used in geometric constructions?