Angle sum of triangle
The first part of this demonstration shows how to construct a triangle using points and line
segments. It shows how to measure the lengths and angles and how to calculate the sum of
the angles in a triangle. The second part looks at the proof of angle sum in a triangle by
adding a line parallel to the base.
Select the point
1. Place three points on the screen
tool.
Either (i) use
arrow select tool
to select points in
the order they are
to be joined or (ii)
with arrow select
tool, drag out a
box around all
three points (hold
down mouse as
the box is
dragged out), or
(iii) use Edit –
select all points
or (iv) use
control A
Either (i) use line
segment tool and
draw line
segments
between vertices,
or (ii) Construct
– segments or
(iii) use Control
L
Measure - length
2. Select the points in order.
3. Join points with line segments. Drag vertices in turn to make the triangle
appear as you want it.
4. Click somewhere on screen to remove all selections. Select one side (with
arrow tool) then measure length. The programme automatically adds the
vertices as you do this. Make sure this measurement is de-selected then repeat
for the other two lengths.
m AB = 5.82 cm
m BC = 7.92 cm
m CA = 9.41 cm
B
C
A
Measure – angle
To change size of
measurement
text, when the
measurement is
selected use Alt >
or Alt <
5. To measure the angles select in turn the three vertices. To measure angle A
select CAB or BAC. Repeat for the other two angles.
mBAC = 55.4
mABC = 91.3
mBCA = 33.3
m AB = 5.17 cm
m BC = 7.74 cm
m CA = 9.41 cm
B
C
A
Measure –
calculate (or Alt
=), select first
angle
measurement
then + select
second angle
measurement and
+ third angle.
6. Sum the three angles using the calculator. Re-label as Total or Angle sum of
triangle. Create a hide/show button.
m AB = 5.17 cm
mBAC = 55
mABC = 91
mBCA = 33
m BC = 7.74 cm
m CA = 9.41 cm
B
Select this total
measurement and
select –
Properties –
Label to change
text and
Properties –
value to display
angles rounded to
nearest unit.
C
A
Angle sum of triangle = 180
Hide Angle Measurement Angle sum of triangle
Select total
measurement
then, Edit –
Action Buttons –
Hide/Show
Construct –
parallel line
7. To demonstrate PROOF of angle sum of triangle:Select one edge as base and opposite vertex. Create line parallel to base
through this vertex. Add two points to the parallel line so that angle between the
parallel line and the edge of the triangle can be measured.
E
B
D
C
A
Angle ABC = 91
Angle DBA = 55
Angle BAC = 55
Angle EBC = 33
Angle BCA = 33
8. Create Hide/Show buttons for each angle. Move the vertices to change the size
and shape of the triangle.