Chapter 13: Q. 28 (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

Step-1 – Given

The given vertices of the quadrilateral are $T (4, 6), A (6, - 4), U (- 4, - 2) and L (- 2, 4)$ .

Step-2 – To determine

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

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:

$\begin{array}{l} T U = \sqrt{{(- 4 - 4)}^{2} + {(- 2 - 6)}^{2}} \\ T U = \sqrt{{(- 8)}^{2} + {(- 8)}^{2}} \\ T U = \sqrt{64 + 64} \\ T U = \sqrt{128} \\ T U = 8 \sqrt{2} \end{array}$

And, the length of AL is:

$\begin{array}{l} A L = \sqrt{{(- 2 - 6)}^{2} + {(4 - (- 4))}^{2}} \\ A L = \sqrt{{(- 2 - 6)}^{2} + {(4 + 4)}^{2}} \\ A L = \sqrt{{(- 8)}^{2} + {(8)}^{2}} \\ A L = \sqrt{64 + 64} \\ A L = \sqrt{128} \\ A L = 8 \sqrt{2} \end{array}$

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

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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

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Proof

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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

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Proof

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Decision Maths

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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.