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3 years ago

9

a side of a square bulletin board measures 34 inches. Which of these is the closest length of a diagonal?

1 answer:

Delicious77 [7]3 years ago

6 0

If you diagonally slice the board, you get a right angle, which pyth thm can be used. side2 x side2 = diagonal2

34squared + 34squared = x (diagonal) squared
1156 + 1156 = x squared
2312 = x squared
x = 48.0832611207
so just correct it to the closest as 48 inches

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The product of two numbers is 30. One of the numbers is t. What expression represents the other number?

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2 years ago

Ipatiy [6.2K]

There are several ways two triangles can be congruent.

$\mathbf{AC = BD}$ <em> congruent by SAS</em>
$\mathbf{\angle ABC \cong \angle BAD}$ <em> congruent by corresponding theorem</em>

In $\mathbf{\triangle AOL}$ and $\mathbf{\triangle BOK}$ (see attachment), we have the following observations

$1.\ \mathbf{AO = DO}$ --- Because O is the midpoint of line segment AD

$2.\ \mathbf{BO = CO}$ --- Because O is the midpoint of line segment BC

$3.\ \mathbf{\angle AOB =\angle COD}$ ---- Because vertical angles are congruent

$4.\ \mathbf{\angle AOC =\angle BOD}$ ---- Because vertical angles are congruent

Using the SAS (<em>side-angle-side</em>) postulate, we have:

$\mathbf{AC = BD}$

Using corresponding theorem,

$\mathbf{\angle ABC \cong \angle BAD}$ ---- i.e. both triangles are congruent

The above congruence equation is true because:

<em>2 sides of both triangles are congruent</em>
<em>1 angle each of both triangles is equal</em>
<em>Corresponding angles are equal</em>

See attachment

Read more about congruence triangles at:

brainly.com/question/20517835

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