Question

Circle P
has diameter MT¯¯¯¯¯¯¯¯¯
. If MT¯¯¯¯¯¯¯¯¯
intersects chord DR¯¯¯¯¯¯¯¯
at E
and m∠TED=90°
, then which of the following statements must also be true?(1 point)
Responses

MD¯¯¯¯¯¯¯¯¯≅TD¯¯¯¯¯¯¯¯

Modifying above upper M upper D with bar congruent to Modifying above upper T upper D with bar

ED¯¯¯¯¯¯¯¯≅ER¯¯¯¯¯¯¯¯

Modifying above upper E upper D with bar congruent to Modifying above upper E upper R with bar

m∠MET=90°

m angle upper M upper E upper T equals 90 degrees

EM¯¯¯¯¯¯¯¯¯≅ET¯¯¯¯¯¯¯

Answer 1

ED ≅ ER.

Reason: MT is a diameter (so the line MT passes through the center). If MT is perpendicular to chord DR at E (given ∠TED = 90°), then a radius/diameter perpendicular to a chord bisects that chord. Thus E is the midpoint of DR, so ED = ER.