Trigonometry

• Theorem: (AAA similarity criterion)

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence, the two triangles are similar.

 

• Theorem: (AA similarity criterion)

If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

 

Example: 

In ΔABC, ∠C is acute, D and E are points on sides BC and AC respectively, such that AD⊥BC and BE⊥AC. Show that BC × CD = AC × CE.

Solution:

 

In ΔADC and ΔBEC,

∠ADC = ∠BEC = 90°

∠DCA = ∠ECB                      [Common]

 By AA similarity criterion, ΔADC ~ ΔBEC

Hence, the result is proved.

• 30°–60°–90° theorem states that “If the angles of a triangle are of measur…