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CTET Straightedge and Compass Construction — practice questions — page 2

Explore 63 free Straightedge and Compass Construction questions in CTET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Straightedge and Compass Construction questions and exercises with answers

Showing questions 31–60 of 63.

The Mohr-Mascheroni theorem says anything constructible with ruler and compass can be built with what alone?Read the answer and worked solution →Which task is impossible with only a ruler and no circle given?Read the answer and worked solution →Which theorem shows a collapsing compass is as powerful as a normal one?Read the answer and worked solution →Which is NOT allowed in a ruler-and-compass construction?Read the answer and worked solution →A valid construction must finish in what kind of number of steps?Read the answer and worked solution →A length can be constructed only if it uses the four operations and what else?Read the answer and worked solution →An angle is constructible only if which of its values is a constructible number?Read the answer and worked solution →Which of these is a standard construction with ruler and compass?Read the answer and worked solution →A circle can be drawn through any three points that are what?Read the answer and worked solution →What does the problem of angle trisection ask you to do?Read the answer and worked solution →Which of these is one of the three famous unsolved Greek problems?Read the answer and worked solution →Which curve did Hippias use in the fifth century BCE to trisect an angle?Read the answer and worked solution →The proof that a 60 degree angle cannot be trisected leads to which kind of equation?Read the answer and worked solution →What must the degree of the minimal polynomial of a constructible number be?Read the answer and worked solution →Which numbers are always constructible from a unit length?Read the answer and worked solution →Any constructible angle theta has an angle of 3 theta that is what?Read the answer and worked solution →The angle 2 pi over N can be trisected if and only if what holds?Read the answer and worked solution →Who first published the impossibility proof of classical angle trisection, in 1837?Read the answer and worked solution →Which tool makes the neusis construction different from classical ones?Read the answer and worked solution →What is Nicomedes known for in the second century BCE?Read the answer and worked solution →Which of these did the Greeks construct from given lengths?Read the answer and worked solution →A Greek could build a square with twice the area of what?Read the answer and worked solution →How long and how marked is the idealized straightedge?Read the answer and worked solution →In a construction, a compass circle is drawn from which two given points?Read the answer and worked solution →Which Euclid proposition gives the bisection of a segment by compass and straightedge?Read the answer and worked solution →Which lines form the boundaries of Voronoi cells?Read the answer and worked solution →The exterior bisector of an angle divides which angle in half?Read the answer and worked solution →The angle bisector theorem compares a side's parts with what?Read the answer and worked solution →A median splits the opposite side of a triangle into two parts that are what?Read the answer and worked solution →Which of these is a ruler-and-compass construction involving a circle?Read the answer and worked solution →

Worked practice questions

The Mohr-Mascheroni theorem says anything constructible with ruler and compass can be built with what alone?

  1. A protractor
  2. A ruler
  3. A set square
  4. A compass
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Correct answer: D. A compass

1. The theorem covers constructions where data and results are discrete points. 2. In that case the compass alone is enough. 3. A ruler alone cannot find a midpoint or take a square root. _Source: Wikipedia, Straightedge and compass construction, section Constructing with only ruler or only compass_

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Which task is impossible with only a ruler and no circle given?

  1. Joining two points
  2. Extending a segment
  3. Marking a midpoint
  4. Drawing a line
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Correct answer: C. Marking a midpoint

1. A ruler can join points and extend lines. 2. Without a circle it cannot mark the midpoint of a segment or take a square root. 3. A single circle with its centre makes these possible (Poncelet-Steiner). _Source: Wikipedia, Straightedge and compass construction, section Constructing with only ruler or only compass_

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Which theorem shows a collapsing compass is as powerful as a normal one?

  1. Angle bisector theorem
  2. Compass equivalence theorem
  3. Pythagorean theorem
  4. Gauss circle theorem
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Correct answer: B. Compass equivalence theorem

1. A collapsing compass cannot directly copy a distance. 2. The compass equivalence theorem, Proposition 2 of Euclid's Book 1, shows no power is lost. 3. So the ideal compass is not required to collapse. _Source: Wikipedia, Straightedge and compass construction, section Straightedge and compass tools_

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