Math

QuestionGiven a polygon PP with angles 125, 35, 250, 80, 135°, identify true statements for any scaled copy QQ of PP.

Studdy Solution

STEP 1

Assumptions1. Polygon has angles of125,35,250,80, and135 degrees. . Polygon $Q$ is a scaled copy of Polygon .

STEP 2

We need to understand the properties of a scaled copy of a polygon. A scaled copy of a polygon is a polygon that has the same shape as the original, but its size is changed by a certain scale factor. The scale factor affects the side lengths of the polygon, but not the angle measures. The angle measures remain the same in a scaled copy.

STEP 3

Let's evaluate each statement\begin{itemize} \item[A.] The side lengths are all whole numbers. \end{itemize}
This statement does not have to be true. The side lengths of a scaled copy of a polygon depend on the scale factor and the original side lengths. They can be whole numbers, but they can also be fractions or irrational numbers.

STEP 4

Evaluate the next statement\begin{itemize} \item[B.] The angle measures are all whole numbers. \end{itemize}
This statement is true. The angle measures of a scaled copy of a polygon are the same as the angle measures of the original polygon. Since the original polygon $$ has angle measures that are all whole numbers, the same is true for any scaled copy $Q$.

STEP 5

Evaluate the next statement\begin{itemize} \item[C.] QQ has exactly1 right angle. \end{itemize}
This statement is not necessarily true. The angle measures of a scaled copy of a polygon are the same as the angle measures of the original polygon. Since the original polygon $$ does not have a right angle, neither does any scaled copy $Q$.

STEP 6

Evaluate the next statement\begin{itemize} \item[D.] If the scale factor between and $Q$ is15 , then each side length of is multiplied by15 to get the corresponding side length of QQ. \end{itemize}
This statement is true. The side lengths of a scaled copy of a polygon are multiplied by the scale factor to get the corresponding side lengths of the scaled copy.

STEP 7

Evaluate the next statement\begin{itemize} \item[E.] If the scale factor is2 , each angle in $$ is multiplied by2 to get the corresponding angle in $Q$. \end{itemize}
This statement is not true. The angle measures of a scaled copy of a polygon are the same as the angle measures of the original polygon. They are not affected by the scale factor.

STEP 8

Evaluate the last statement\begin{itemize} \item[F.] QQ has2 acute angles and3 obtuse angles. \end{itemize}
This statement is true. The original polygon $$ has2 acute angles (35 and80 degrees) and3 obtuse angles (125,250, and135 degrees). Since the angle measures of a scaled copy of a polygon are the same as the angle measures of the original polygon, the same is true for any scaled copy $Q$.
So, the statements that must be true for any scaled copy QQ of Polygon $$ are B, D, and F.

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