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 EM¯¯¯¯¯¯¯¯¯≅ET¯¯¯¯¯¯¯ Modifying above upper E upper M with bar congruent to Modifying above upper E upper T with bar MD¯¯¯¯¯¯¯¯¯≅TD¯¯¯¯¯¯¯¯ Modifying above upper M upper D with bar congruent to Modifying above upper T upper D with bar m∠MET=90° m angle upper M upper E upper T equals 90 degrees ED¯¯¯¯¯¯¯¯≅ER¯¯¯¯¯¯¯¯

Answer 1

Given that MT is the diameter of circle P and intersects chord DR at E with m∠TED = 90°, you can deduce the following key points based on the properties of circles:

1. A diameter that intersects a chord at a right angle (90 degrees) implies that the point of intersection (E) is the midpoint of the chord (DR).

Since E is the midpoint of DR, we can conclude that:

• ED ≅ ER (the segments from E to D and from E to R are equal).

As for the other statements provided, here’s an analysis:

• EM ≅ ET: This statement cannot be concluded just from the information provided. We do not have enough data to prove that EM and ET are congruent.

• MD ≅ TD: This statement cannot be established directly since we don't have information that relates specifically to segments MD and TD

• m∠MET = 90°: This statement is also not guaranteed based on the information about E.

• ED ≅ ER: This is true. As previously discussed, E is the midpoint of chord DR, therefore ED is congruent to ER.

Thus, the statement that must also be true is:

ED ≅ ER.