Math

QuestionIdentify true statements for a scaled copy QQ of polygon PP: A) whole number sides, B) whole number angles, D) side lengths scaled by 15\frac{1}{5}.

Studdy Solution

STEP 1

Assumptions1. Polygon is a given polygon with certain side lengths and angles. . Polygon $Q$ is a scaled copy of Polygon .
3. The scale factor between $$ and $Q$ can vary.

STEP 2

Let's analyze each statement one by one.
Statement A The side lengths are all whole numbers.
This statement does not necessarily have to be true. The side lengths of QQ will depend on the side lengths of andthescalefactor.Ifthesidelengthsof and the scale factor. If the side lengths of or the scale factor are not whole numbers, then the side lengths of QQ will not be whole numbers.

STEP 3

Statement B The angle measures are all whole numbers.
This statement also does not necessarily have to be true. The angle measures of QQ will be the same as those of ,regardlessofthescalefactor.Iftheanglemeasuresof, regardless of the scale factor. If the angle measures of are not whole numbers, then the angle measures of QQ will not be whole numbers.

STEP 4

Statement C QQ has exactly1 right angle.
This statement does not necessarily have to be true. The number of right angles in QQ will be the same as the number of right angles in ,regardlessofthescalefactor.If, regardless of the scale factor. If does not have exactly1 right angle, then QQ will not have exactly1 right angle.

STEP 5

Statement D If the scale factor between and $Q$ is $\frac{1}{5}$, then each side length of is multiplied by 15\frac{1}{5} to get the corresponding side length of QQ.
This statement is true. The side lengths of a scaled copy are multiplied by the scale factor to get the corresponding side lengths. Therefore, if the scale factor is 15\frac{1}{5}, then each side length of $$ is indeed multiplied by $\frac{1}{5}$ to get the corresponding side length of $Q$.

STEP 6

Statement If the scale factor is2 , each angle in $$ is multiplied by2 to get the corresponding angle in $Q$.
This statement is not true. The angles of a scaled copy are the same as the angles of the original polygon, regardless of the scale factor. Therefore, the angles in $$ are not multiplied by2 to get the corresponding angles in $Q$.

STEP 7

Statement F QQ has2 acute angles and3 obtuse angles.
This statement does not necessarily have to be true. The number and types of angles in QQ will be the same as those in ,regardlessofthescalefactor.If, regardless of the scale factor. If does not have2 acute angles and3 obtuse angles, then QQ will not have2 acute angles and3 obtuse angles.
So, the only statement that must be true for any scaled copy QQ of Polygon $$ is Statement D.

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