Question

If line WP is a median and an angle bisector, AP = 3y+11, PH = 7y - 5, angle HWP = x +12, angle PAW = 3x - 2, and angle HWA = 4x - 16, find x and y. Is WP also an altitude? Explain.

Answer 1

∠ HWA / 2 = ∠HWP
( 4 x - 16 ) / 2 = x + 12
4 x - 16 = 2 x + 24
2 x = 40
x = 20
AP = PH
3 y + 11 = 7 y - 5
16 = 4 y 
y = 4
∠PAW = 60 - 2 = 58°
∠PWA = 32°, ∠PWH = 32°
∠AWH = 64°
∠WHA = 58°
     Therefore Δ AWH is isosceles. Line WP is an altitude because it bisects the base of an isosceles triangle.