Answered

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will mark brainliest In a quadrilateral ABCD, the diagonals intersect at point T. Heather has used the Alternate Interior Angles Theorem to show that angle ABD is congruent to angle CDB and that angle BAC is congruent to DCA.

Which of the following can Heather use prove that segment DT is equal to segment TB?

AB ≅ DC
AC ≅ DB
DA ≅ BC
AC ≅ AC

Sagot :

mathstudent55

Answer:

segment AB ≅ segment DC

Step-by-step explanation:

If the statement of the problem is correct, and ABCD is a quadrilateral, but we are not told it is a parallelogram, then you cannot use the Alternate Interior Angle Theorem.

Assume ABCD is a parallelogram.

By using the Alternate Interior Angle Theorem twice and having

<ABD ≅ <CDB and

<BAC ≅ <DCA,

then since segment AB ≅ segment DC (opposite sides of a parallelogram), then

triangle ATB ≅ triangle CTD by ASA,

and by CPCTC,

segment DT ≅ segment TB

Answer: segment AB ≅ segment DC

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