Back to Exercise: Constructing and Bisecting Line Segments and Angles

Exercises: Constructing and Bisecting Line Segments and Angles

Use only a pair of compasses and a straight edge to construct — a protractor may only be used to check your work afterward.

Grade 7·15 problems·~24 min·Uganda NCDC Primary 7 Mathematics·lesson·construction-02

Printable layout

Recall / Warm-Up

Review the difference between constructing and measuring before bisecting anything.

Asked to construct a $60\degree$ angle, which method actually counts as constructing?

Measuring $60\degree$ directly with a protractor and marking the ray

Drawing the angle by eye, then labeling it $60\degree$

Drawing arcs with a pair of compasses using the equilateral-arc method

To copy a segment $AB$ with a pair of compasses, what do you do first?

Draw a fresh line first, then guess a matching length by eye

Set the compass point on $A$ and the pencil on $B$ , to capture the length

Measure $AB$ with a ruler first, then set the compass to that ruler reading

Fluency Practice

You copy segment $AB = 9$ cm onto a fresh line starting at point $C$ , using the compass capture-and-mark method (no ruler reading). What is the length of the copied segment $CD$ ?

$Perpendicular bisector construction of segment AB showing equal arcs from A and B crossing above and below, with the bisecting line meeting AB at a right angle$

You construct the perpendicular bisector of $AB = 10$ cm using equal arcs from $A$ and from $B$ . What TWO facts does the resulting line give you about $AB$ ?

It only finds the midpoint of $AB$ ; the right angle needs a separate construction

It cuts $AB$ at its midpoint AND meets $AB$ at $90\degree$ — both from the same construction

It only produces a right angle at one end of $AB$ , not the midpoint

$An 80-degree angle at vertex O with a single arc from the vertex crossing both arms at points P and Q$

To bisect an $80\degree$ angle at vertex $O$ , where do you strike the FIRST arc from?

From vertex $O$ , cutting both arms of the angle

From the two points where the angle's arms end, at their far tips

From the midpoint of the angle's two arms, one arc for each

You bisect a constructed $90\degree$ angle using the compass method. What angle results from each half?

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