Questions and Answers
Which of the following are parts of a construction problem? (Select all that apply)
What are two key terms relating to a locus of points?
What is the construction for dividing a line into 5 equal segments?
Construction 1
What is the construction for constructing a tangent to the circle from point R (outside the circle)?
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What is the construction for circumscribing a circle about the given triangle?
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What is the construction for constructing a tangent to circle O at point P (on the circle)?
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What is the construction for constructing a right triangle given a leg and its opposite acute angle?
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What is the construction for constructing an isosceles triangle with the given leg and base?
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What is the locus of points outside a circle with a radius that is d units longer than the given circle?
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What is the locus of the centers of all circles that are tangent to both parallel lines?
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What is the locus of points in the interior of square ABCD and equidistant from its sides AB and BC?
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What is the locus of points that is two inches from a given line and also three inches from a given point in that line?
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What is the locus of points equidistant from points A and B (six inches apart), which are also five inches away from point A?
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What is the locus of points that is equidistant from two circles and also at a distance of eight inches from line AB?
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Study Notes
Key Components of Construction Problems
- Four essential parts: Given, Required, Construction, Proof.
Locus of Points
- Inclusive & Exclusive: Terms relating to the definition and parameters of a locus of points.
Geometric Constructions
- Construction 1: Method to divide a line into five equal segments.
- Construction 2: Technique to construct a tangent line from an external point R to a circle.
- Construction 3: Procedure for circumscribing a circle around a given triangle.
- Construction 4: Method to create a tangent line to circle O at point P, which lies on the circle.
- Construction 5: Steps to build a right triangle when a leg and the opposite acute angle are provided.
- Construction 6: Technique to construct an isosceles triangle with specified leg length and base.
Loci Related to Circles and Lines
- Locus of points outside a circle: Defined as a circle concentric to the original with a radius that is d units larger.
- Locus of centers of tangent circles: A line parallel to two given lines, situated midway between them.
Interior Points and Distances
- Distance and Location: The locus of points within square ABCD that are equidistant from sides AB and BC relates to diagonal BD (excluding points B and D).
- Complex Loci: Defined by conditions such as two inches away from a line and three inches from a point.
Perpendicular and Equidistant Points
- Locus formed by intersections: Two points where the perpendicular bisector of segment AB intersects with a circle centered at point A with a radius of 5 inches.
- Locus of points equidistant from two circles: Defined by a circle that is concentric to the original circles and set parallel lines eight inches away from line AB.
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Description
Prepare for your Geometry Test with these review flashcards. Each card contains essential terms and definitions related to construction problems and geometric concepts. Great for reinforcing your understanding before the test!
