Similar triangles:
The third criterion of similarity.
4th year of secondary education - Option A.
 
The third criterion of similar triangles.

Two triangles are similar if two pairs of sides are in the same ratio and the included angles are equal.

Change the size of the triangles by dragging the red points with the mouse. You can also alter the value of angles B and C.

Here are two triangles which are once again in Thales' position. As you can see, both triangles share angle B and their pairs of sides are in the same ratio.

Activity 7.

A vertical post 3 metres high produces a shadow 2 metres high. How tall is a tree that produces a shadow 4.5 metres high at the same time? (Draw a picture to illustrate the problem).

Activity 8.

A triangle has sides that measure 30, 40 and 50 cm respectively. A second triangle has sides that measure 12, 16 and 20 cm. Are they similar? If so, what is their ratio?

Change the size of the triangles by dragging points C or F with the mouse.
Activity 9.

As you can see, these two triangles are similar. Sides c-f and a-d are in the same ratio. The included angles B and E both measure 90º. Find out the ratio of similitude and lengths of the other sides.

       
           
  Máximo Prudencio Conejo
 
Spanish Ministry of Education. Year 2001