Given <BCA is congruent to <EFD, segment BA is perpendicular to segment AD, segment ED is perpendicular to segment AD, and segment AC is congruent to segment DF.

Question

Given <BCA is congruent to <EFD, segment BA is perpendicular to segment AD, segment ED is perpendicular to segment AD, and segment AC is congruent to segment DF.

Prove: segment BC is congruent to segment EF.

Answer 1

Hi Lei,

since I don’t have a figure, I can only try to help with whatever you have given.

you will have two triangles ABC and DEF with right angles at A and D?

Given: <BCA congruent to <EFD

Given: segment AC congruent to segment DF

we have to show that angle <BAC and <EDF are right angles from other information provided

now you have two congruent triangles from ASA congruence theorem

hence you can prove that segment BC is congruent to segment EF by CPCTC

does that help?