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Use the 45-45-90 pattern to find both missing side lengths of each right triangle:

Choices
20
:". 14

5sqrt2
16
5

10sqrt2

7sqrt2
3)

8sqrt2
7
9

14sqrt2
5)
6)

$1$ . Use the $45$ $-45$ $-90$ pattern to find both missing side lengths of each right triangle: $\newline$ $1$ ) $\newline$ $2$ ) $\newline$ Choices $\newline$ $20$ $\newline$ :

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Estimate positive square roots

Full solution

Q.

1

. Use the

45

-45

-90

pattern to find both missing side lengths of each right triangle:

\newline

1

)

\newline

2

)

\newline

Choices

\newline

20

\newline

:

Identify Properties: Identify the properties of a $45$ $-45$ $-90$ triangle. In such triangles, the legs are congruent and the hypotenuse is $\sqrt{2}$ times the length of each leg.
Calculate Hypotenuse: Assume one leg of the triangle is given as $5$ . Calculate the hypotenuse using the $45$ $-45$ $-90$ rule: Hypotenuse = $5 \times \sqrt{2}$ .
Check Choices: Check if $5\sqrt{2}$ is listed in the choices. Yes, it is listed as a choice.
Verify Other Leg: Since both legs are the same in a $45-45-90$ triangle, the other leg is also $5$ . Check if $5$ is listed in the choices. Yes, it is listed as a choice.

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