Question

decide whether each statement about the example is true or false. true false $overline{pq}$ is congruent to $overline{pq}$. true false $overline{pq}$ is perpendicular to $overleftrightarrow{bc}$. true false $moverline{qq}
eq moverline{tr}$ true false $moverline{pp}
eq moverline{tr}$ true false $overleftrightarrow{tr}paralleloverleftrightarrow{qq}$ complete the statement about the example. line segment $pq$ was in the direction a distance

Explanation:

1. For the statement " $\overline{P'Q'}$ is congruent to $\overline{PQ}$":

• # Explanation:
• ## Step1: In a transformation (such as translation, rotation, reflection), the length of a line - segment is preserved. If $\overline{P'Q'}$ is the image of $\overline{PQ}$ under a rigid transformation, their lengths are equal.
• By the definition of congruent line - segments (line - segments with equal lengths), if a transformation is rigid (preserves distance), $\overline{P'Q'}\cong\overline{PQ}$.
• # Answer: True

1. For the statement " $\overline{P'Q'}$ is perpendicular to $\overleftrightarrow{BC}$":

• # Explanation:
• ## Step1: There is no information given about the relationship between $\overline{P'Q'}$ and $\overleftrightarrow{BC}$. Without any details about angles formed or geometric properties related to these two elements, we cannot assume perpendicularity.
• We need angle measurements or other geometric facts to determine perpendicularity.
• # Answer: False

1. **For the statement " $m\overline{QQ'}

eq m\overline{TR}$":**

• # Explanation:
• ## Step1: There is no information given about the lengths of $\overline{QQ'}$ and $\overline{TR}$. Without any data on their lengths, we cannot say they are not equal.
• We have no basis for comparing their measures.
• # Answer: False

1. **For the statement " $m\overline{PP'}

eq m\overline{TR}$":**

• # Explanation:
• ## Step1: There is no information given about the lengths of $\overline{PP'}$ and $\overline{TR}$. Without any data on their lengths, we cannot say they are not equal.
• We have no basis for comparing their measures.
• # Answer: False

1. For the statement " $\overleftrightarrow{TR}\parallel\overleftrightarrow{QQ'}$":

• # Explanation:
• ## Step1: There is no information given about the orientation or relationship between $\overleftrightarrow{TR}$ and $\overleftrightarrow{QQ'}$. Without angle - related information or other geometric properties, we cannot assume parallelism.
• We need angle - congruence or other parallel - line criteria to determine parallelism.
• # Answer: False

Answer:

1. For the statement " $\overline{P'Q'}$ is congruent to $\overline{PQ}$":

• # Explanation:
• ## Step1: In a transformation (such as translation, rotation, reflection), the length of a line - segment is preserved. If $\overline{P'Q'}$ is the image of $\overline{PQ}$ under a rigid transformation, their lengths are equal.
• By the definition of congruent line - segments (line - segments with equal lengths), if a transformation is rigid (preserves distance), $\overline{P'Q'}\cong\overline{PQ}$.
• # Answer: True

1. For the statement " $\overline{P'Q'}$ is perpendicular to $\overleftrightarrow{BC}$":

• # Explanation:
• ## Step1: There is no information given about the relationship between $\overline{P'Q'}$ and $\overleftrightarrow{BC}$. Without any details about angles formed or geometric properties related to these two elements, we cannot assume perpendicularity.
• We need angle measurements or other geometric facts to determine perpendicularity.
• # Answer: False

1. **For the statement " $m\overline{QQ'}

eq m\overline{TR}$":**

• # Explanation:
• ## Step1: There is no information given about the lengths of $\overline{QQ'}$ and $\overline{TR}$. Without any data on their lengths, we cannot say they are not equal.
• We have no basis for comparing their measures.
• # Answer: False

1. **For the statement " $m\overline{PP'}

eq m\overline{TR}$":**

• # Explanation:
• ## Step1: There is no information given about the lengths of $\overline{PP'}$ and $\overline{TR}$. Without any data on their lengths, we cannot say they are not equal.
• We have no basis for comparing their measures.
• # Answer: False

1. For the statement " $\overleftrightarrow{TR}\parallel\overleftrightarrow{QQ'}$":

• # Explanation:
• ## Step1: There is no information given about the orientation or relationship between $\overleftrightarrow{TR}$ and $\overleftrightarrow{QQ'}$. Without angle - related information or other geometric properties, we cannot assume parallelism.
• We need angle - congruence or other parallel - line criteria to determine parallelism.
• # Answer: False