Example 8

Transcript

Example 8 P is a point equidistant from two lines l and m intersecting at point A (see figure). Show that the line AP bisects the angle between them. Given: PB = PC & ∠ PBA = ∠ PCA = 90° To prove: ∠ PAB = ∠ PAC Proof In Δ PAB and Δ PAC. ∠ PBA = ∠ PCA PA = PA PB = PC So, Δ PAB ≅ Δ PAC ∴ ∠ PAB = ∠ PAC Hence proved.