Prove the Following:

Question

In the figure A, B, C and D are non-coplanar points with B, C, and D in the plane E. Show that if AB ⊥ BD, and BC=BD, then AC=AD

Answer 1

AB is perpendicular to DB is given

then angles ABD is 90 degree right angle

angle ABD and ABC are linear pair

so angle ABC + angle ABD = 180 becuase they are supplementary

angle ABC + 90 = 180 by subsitution

angle ABC = 90 by subtraction property of equality

angle ABC is right angle by defintion

AB is perpendicular to BC by defintion

then angle ABC = angle ABD = 90 by substitution/transitive

BC = BD is given

AB = AB by reflexive property

triangle ABC is congruent to triangle ABD by leg-leg and SAS

AC = AD by CPCTC