- 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.
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.
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…
To view the complete topic, please