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…

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