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Question 1 of 10
1. Question
Construct triangle ABC in which |AB| = 5 cm, |AC| = 6 cm, and |BC| = 9 cm. Construct the bisector of angle B. Construct the perpendicular bisector of BC. The bisectors meet at O. Measure |OC|.
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Question 2 of 10
2. Question
Use ruler and compasses to construct triangle PQR in which angle Q = 90 degrees, |QR| = 5 cm, and |PR| = 10 cm. Measure |PQ|. Use Pythagoras’ theorem to check the result.
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Question 3 of 10
3. Question
Construct triangle ABC such that |AB| = 8 cm, |BC| = 11 cm, and |AC| = 10 cm. Mark a point X on side AB such that |BX| = 5 cm. Use a ruler and set square to construct a line through X parallel to side BC to meet side AC at Y. Measure |XY| and |CY|.
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Question 4 of 10
4. Question
Construct quadrilateral ABCD such that |AB| = 5 cm, |BD| = |DC| = 8 cm. Angle ABD = 30 degrees and Angle BCD = 45 degrees. Measure the diagonal |AC|.
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Question 5 of 10
5. Question
Construct a triangle ABC such that AB = 7 cm, BC = 9 cm, and AC = 8 cm. Construct the perpendicular bisector of BC to meet AC at D. Measure |CD| and |AD|.
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Question 6 of 10
6. Question
Using a ruler and a pair of compasses only, construct triangle XYZ, such that |XY| = 10 cm, |YZ| = 8 cm, and |XZ| = 6 cm. Construct the mediator of XZ to meet XY at M. Measure |YM|.
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Question 7 of 10
7. Question
Construct a triangle ABC with AB = 6 cm, BC = 8 cm, and AC = 7 cm. Locate by construction the point P inside triangle ABC which is equidistant from AB and AC and also 5 cm from BC. Measure |AP|.
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Question 8 of 10
8. Question
Construct a rectangle PQRS such that |PQ| = 8 cm and |QR| = 6 cm. Construct the locus of points equidistant from PQ and QR. Construct the locus of points 5 cm from R. The loci intersect at T. Measure |PT|.
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Question 9 of 10
9. Question
Using a ruler and a pair of compasses only: a. Construct a triangle ABC such that |AB| = 8 cm, |BC| = 6 cm, and ∠ABC = 60°. b. Locate by construction the point X, inside △ABC, which is equidistant from BA and BC. c. Construct the locus of points inside △ABC which are 3 cm from AC. d. Locate by construction the point Y, inside △ABC, which is 3 cm from AC and equidistant from BA and BC. e. Measure |AY| and |XY|.
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Question 10 of 10
10. Question
Construct a quadrilateral ABCD in which AB = 4 cm, BC = 7 cm, AD = 5 cm, ∠ABC = 135°, and ∠BAD = 60°. (a) Measure: (i) |BD| (ii) |CD|. (b) Construct the locus of points inside the quadrilateral which are equidistant from B and D. (c) Construct the locus of points inside the quadrilateral which are 3 cm from BC. (d) Locate the point, X, inside the quadrilateral such that it is 3 cm from BC and equidistant from B and D.
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