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Chapter 13: Q. 28WE (page 527)

In Exercises 27-32 find and then compare lengths of segments.

Quadrilateral TAUL has vertices T(4, 6), A(6, -4), U(~4, -2), and L(-2, 4), Show that the diagonals are congruent.

Short Answer

Expert verified

The diagonals are congruent.

Step by step solution

01

Step-1 – Given

The given vertices of the quadrilateral areT4,6,A6,鈭�4,U鈭�4,鈭�2andL鈭�2,4

02

Step-2 – To determine

We have to show that the diagonals of the quadrilateral are congruent.

03

Step-3 – Proof

The diagonals are TU and AL. We will use the distance formula to show TU = AL.

Using the distance formula, the length of TU is:

TU=鈭�4鈭�42+鈭�2鈭�62TU=鈭�82+鈭�82TU=64+64TU=128TU=82

And, the length of AL is:

AL=鈭�2鈭�62+4鈭�鈭�42AL=鈭�2鈭�62+4+42AL=鈭�82+82AL=64+64AL=128AL=82

So, TU = AL so, the diagonals of the quadrilateral are congruent.

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Most popular questions from this chapter

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