1. Similar triangles
If I take a triangle that is 3cm x 4cm x 5cm and hold it in front of a light.
I can project a much larger image on a distant wall
3m x 4m x 5m
These triangle are similar, so their measurements are proportional .

2. Similar triangles
If I move the projector closer to the wall the image on the wall shrinks
But it will still be proportional
15cm x 20 cm x 25 cm
The angles of the two triangles are equal
If I cut the base of the large triangle in half with a line parallel to the left side
The right side of the old triangle will create a new similar triangle
7.5cm x 10cm x 12.5cm
Each of these measurement is ½ the previous measurements
The ratio between the two triangles is 1:2
Another way to express the ratio is ½ .

3. Similar triangles
We can simplify many seemingly difficult questions simply by discovering similarity of triangles
When we know the ratio or recognize it easily we have solved 90% of the problem.
A 6ft man casts 5 ft shadow next to a flagpole that is casting a 20 foot shadow.
How tall is the flagpole ?
6/5 equals x/20
Two easy ways to solve
I multiplied 5 x 4 to get 20
Do the same for six (6 x 4 = 24)
Another method . ? 6 5 20

4. Similar triangles
Questions from Triand MCAS test

5. Similar triangles
Questions from Triand MCAS test