Question

Given: ABC , BD is an
altitude to side AC, & D is a midpoint
Prove: AB BC

Answer 1

Explanation:

BD is an altitude given

D is midpoint of AC given

BD ⊥ AC an altitude is a perpendicular segment

from a vertex to the opposite side

AD = DC because BD is a perpendicular bisector

BD = BD reflexive property

∠ADB ≅ ∠CDB because BD ⊥ AC

ΔADB ≅ ΔCDB SAS

AB ≅BC corresponding sides of congruent triangles

are congruent

Answer 2

steps below

Explanation:

BD⊥AC ∠ADB = ∠CDB = 90°

D is mid-point: AD = CD

BD = BD

ΔADB ≅ ΔCDB

AB = BC