Geometry (Classes VI–VIII) • Topic 6 of 6

Practical Geometry (Construction)

Practical geometry is construction with a compass and straight-edge (and, in school, a protractor and set squares): copying a line segment, drawing a perpendicular, bisecting a segment or an angle, and constructing triangles and simple quadrilaterals from given measurements. The two foundational constructions CTET keeps returning to are the perpendicular bisector of a segment (every point on it is equidistant from the two endpoints) and the angle bisector. A 60° angle is constructed with the compass alone (the equilateral-triangle arc method), without a protractor — a fact CTET likes to check. The pedagogy is about why we do constructions at all: they make abstract properties tangible, build fine motor skill and precision, and let a child verify a property (e.g. that the bisector really halves the angle) by doing rather than being told — a hands-on bridge from van Hiele Level 1 to Level 2. The classic misconceptions are changing the compass width mid-construction, and believing every construction needs a protractor. CTET tests which tool/method gives a particular construction, what the perpendicular bisector guarantees, and the teaching rationale for construction work.

✅ Solved examples

1. Which construction has the property that every point on it is equidistant from the two endpoints of a line segment?
The perpendicular bisector of the segment. It cuts the segment at its midpoint at 90°, and any point on it is the same distance from both endpoints.
2. A teacher wants pupils to construct a 60° angle. Which instrument is essential for the standard construction?
A compass (with a straight-edge). The 60° angle is made by drawing an arc and stepping the same radius along it — the equilateral-triangle method — so no protractor is required.
3. Why is hands-on construction valued in the Class VI–VIII geometry classroom?
It turns abstract properties into something the child does and verifies physically (e.g. that an angle bisector truly halves the angle), building precision and motor skill and moving the learner from simply seeing shapes to reasoning about their properties.
4. A pupil bisects a 90° angle correctly. What is the measure of each of the two new angles?
An angle bisector splits an angle into two equal parts, so each new angle = 90° ÷ 2 = 45°.

✏️ Practice — try these, take hints as needed

1. The line that divides a given angle into two equal angles is called the:
It bisects the angle.
Not the perpendicular bisector.
Angle bisector
2. To construct a 60° angle using only a compass and straight-edge, you draw an arc and then:
Keep the same radius.
Step the radius along the arc.
Mark off the same radius on the arc (equilateral-triangle method)
3. The perpendicular bisector of a 10 cm segment meets it at a distance of ___ cm from each endpoint.
It passes through the midpoint.
Half of 10.
5 cm
4. A common pupil error during construction that ruins the figure is:
Something about the compass.
It must stay fixed.
Changing the compass width (radius) midway through

📝 Topic test — 8 questions

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