Geometry: loci and constructions — KCSE Mathematics

KCSE Mathematics · 100 practice questions · 3 syllabus objectives

31 easy34 medium35 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define locus and describe common loci (perpendicular bisector, angle bisector, circle, parallel line)

Construct geometric figures (perpendicular bisector, angle bisector, circumscribed/inscribed circles, regular polygons) using ruler and compass only

Geometry: loci and constructions

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easySHORT ANSWER4 marks

State the steps to construct the angle bisector of angle ABC using a ruler and compass only. (4 marks)

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Part (a) — 4 marks

Place the compass at point B and draw an arc that intersects both sides of the angle (1 mk)

Label the intersection points as D and E (1 mk)

With the same radius, draw arcs from points D and E (1 mk)

Draw a straight line from B to the intersection of the two arcs (1 mk)

easySHORT ANSWER2 marks

State the locus of points that are all equidistant from two fixed points A and B. (2 marks)

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Part (a) — 2 marks

The locus is the perpendicular bisector of the line segment AB (1 mk)

It is a straight line that divides segment AB into two equal parts at right angles (1 mk)

easySHORT ANSWER4 marks

Describe the method to construct a circle that is inscribed in triangle XYZ. (4 marks)

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Part (a) — 4 marks

Construct the angle bisectors of two angles in triangle XYZ (1 mk)

Label the intersection of the two angle bisectors as point G (1 mk)

Using a compass, measure the distance from G to one side of the triangle (1 mk)

Draw a circle centred at G with the measured radius to touch all three sides of the triangle (1 mk)

Name the steps to construct the angle bisector of angle ABC using only a ruler and compass. (3 marks)

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