Year 9 · Constructions and congruence
Draw and measure angles accurately
Learn how to measure and draw angles accurately, construct exact right angles with compasses, and find missing lengths and angles in similar shapes.
Definition
An angle measures an amount of turn between two lines, in degrees, and a protractor lets you measure or draw one to the nearest degree. A construction goes further: it builds an exact figure using only compasses and a straight edge, so a right angle made this way is exact rather than estimated. Two shapes are similar when one is an enlargement of the other. Their angles match exactly, and every length in one shape is the same multiple of the matching length in the other.
Why Do I Have to Learn This?
Angles measure turn, from door hinges to skate ramps. Reading them helps you build, draw and navigate accurately.
Key Rules:
- 1. To measure or draw an angle, place the protractor's centre on the point of the angle, line up the zero line with one arm, and read the scale that starts at zero on that arm.
Remember:
- •One compass setting builds an exact right angle. In similar shapes, lengths multiply by the scale factor and angles stay the same.
Don’t Forget...
- •Reading the wrong protractor scale and recording a 50 degree angle as 130 degrees. A protractor carries two scales running in opposite directions. Use the one that reads zero on the arm you lined up, and check the reading against whether the angle looks acute or obtuse.
Acute angle
An angle smaller than 90 degrees.
An angle of 45° is acute.
Worked Example:
Construct the perpendicular bisector of a line segment AB that is 8 cm long.
Set your compasses to more than half of AB. Half of 8 cm is 4 cm, so a 5 cm setting works.
Put the compass point on A and draw an arc above the line and an arc below it.
Keep the same 5 cm setting, put the point on B and draw two more arcs so they cross the first pair.
Join the two crossing points with a ruler.
Answer: The new line crosses AB at right angles, exactly 4 cm from each end.
Why It Works:
Each arc crossing is the same distance from A as from B, because both pairs of arcs used the same compass setting, and every point that is equally far from the two ends of a segment lies on the line that cuts it in half at right angles. Similar shapes are enlargements of each other, and an enlargement multiplies every length by the same scale factor while leaving every angle unchanged.
Another Example:
Triangles PQR and XYZ are similar, with P matching X, Q matching Y and R matching Z. PQ = 6 cm, XY = 9 cm, QR = 8 cm and angle P = 40 degrees. Find YZ and angle X.
Find the scale factor from PQR to XYZ using the matching sides PQ and XY: 9 divided by 6 = 1.5.
YZ matches QR, so YZ = 8 x 1.5 = 12 cm.
Angles are not scaled in similar shapes, so angle X = angle P = 40 degrees.
Answer: YZ = 12 cm and angle X = 40 degrees.
Animated Example:
Free Draw and measure angles accurately Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Let’s Practise the Concept
Step 1 of 3
Put the angles in order
Tap them from smallest to largest.
In order so far: nothing yet