Download Triangles Investigation 2

Investigating Triangles 2
Investigating Sides and Angles
We are learning about the properties of right angled triangles
Equipment required: Paper, ruler, calculator, protractor
EA
AA
AM
AP+
Prior knowledge:
 Using a ruler and a protractor
 The concept of similar shapes
 The hypotenuse
 The relationship between division and fractions
 The relationship between fractions and decimals
Task
You are to investigate some sets of similar triangles. Start with the sets used
in the activity “developing similarity”, and make up some more if you need more
to.
This time you are to look at triangles differently, comparing both sides and angles.
The angle
opposite
AC
adjacent
Things to do
1)
Draw to scale (or find) a set of 3 similar triangles. Write how long the sides
are next to each side.
2)
Label one angle (not the right angle), making sure it is the same angle in each
of the triangles. Measure this angle for each triangle to check it the same.
3)
Label the side opposite the angle and next to (adjacent to) the angle with
these words. (Opposite and adjacent seem good names to use)
4)
For each triangle in the set, measure the angle and work out the fraction
opposite
made by dividing size of the opposite by the size of the adjacent.
adjacent
5)
6)
7)
Simplify the fractions and convert them to decimals.
Repeat the above for 2 other sets of similar triangles
Write up your findings. In this, try to use the word RATIO, as the fraction
found by dividing the length of the opposite by the length of the adjacent
compares the lengths of the two sides. We often say it finds the ratio of the
two sides.
More to try
The hypotenuse is the longest side in a right angled triangle. Repeat the exercise
above, using the same triangles, but this time divide the length of the opposite side
by the length of the hypotenuse. What have you found out this time? Be prepared
to report your findings to the rest of the group.