Angles of a triangle: building a roof frame
Turn the two rafters of a roof frame and see how the angle at the ridge always makes the three angles add up to 180°.
Core concept
In short: Build a roof and see that a triangle's three angles always add up to 180°.
The three angles of any triangle add up to 180°
Topic: Triangles and angles
A roof frame (truss) is a triangle: a tie beam across the walls and two rafters that meet at the ridge. A carpenter chooses how steeply each rafter rises from the beam; these are the two base angle: The amount of turn between two lines that meet, measured in degrees (°). All key words. The angle at the ridge is then fixed, because the three angles of every triangle add up to 180°. Triangles are named by their angles (acute, right or obtuse) and by their sides: equilateral (all sides equal), isosceles (two sides equal) or scalene (no sides equal). Equal angles sit opposite equal sides.
What you will learn
- Show that the angles of a triangle add up to 180°.
- Find the third angle of a triangle from the other two.
- Name triangles by their angles and by their sides.
Before you start
- Read an angle in degrees.
Materials
- A paper triangle to tear the corners off
Equipment
- A protractor
Procedure
- Drag a rafter to turn it and change the angle it makes with the beam.
- Watch the angle at the ridge and the three corners laid side by side on a straight line.
- Record an equilateral roof, a right-angled roof and an obtuse-angled roof.
- Make the rafters so steep that they never meet, and record it.
How this simulation is simplified
- The beam is 6 m long and the rafters are straight.