QuestionDivide the line segment $\overline{P Q}$ into four equal parts using a compass and straightedge. Choose the correct method.

Studdy Solution

STEP 1

Assumptions1. We have a line segment $\overline{ Q}$ . . We have a compass and a straight edge.
3. We want to divide $\overline{ Q}$ into four congruent segments.

STEP 2

To divide $\overline{ Q}$ into four congruent segments, we need to find the midpoint of $\overline{ Q}$ first. We can do this by constructing the perpendicular bisector of $\overline{ Q}$ .

STEP 3

To construct the perpendicular bisector of $\overline{ Q}$ , we first place the point of the compass at point $$ and draw an arc that is more than half way to $Q$. Without changing the compass width, we then place the point of the compass at point $Q$ and draw another arc that intersects the first arc.

STEP 4

We then draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{ Q}$ . We label the point where this line intersects $\overline{ Q}$ as $M$ .

STEP 5

Now, we have divided $\overline{ Q}$ into two congruent segments, $\overline{ M}$ and $\overline{M Q}$ .

STEP 6

We repeat the process for $\overline{ M}$ and $\overline{M Q}$ to divide them each into two congruent segments.

STEP 7

For $\overline{ M}$ , we place the point of the compass at point $$ and draw an arc that is more than half way to $M$. Without changing the compass width, we then place the point of the compass at point $M$ and draw another arc that intersects the first arc.

STEP 8

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{ M}$ . We label the point where this line intersects $\overline{ M}$ as $$.

STEP 9

We repeat the process for $\overline{M Q}$ . We place the point of the compass at point $M$ and draw an arc that is more than half way to $Q$ . Without changing the compass width, we then place the point of the compass at point $Q$ and draw another arc that intersects the first arc.

STEP 10

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{M Q}$ . We label the point where this line intersects $\overline{M Q}$ as $$.

STEP 11

Now, we have divided $\overline{ Q}$ into four congruent segments $\overline{ N}$ , $\overline{ M}$ , $\overline{M O}$ , and $\overline{ Q}$ .
So, the correct answer is A. Construct the perpendicular bisector of $\overline{ Q}$ and label its midpoint $M$ . Repeat this process for $\overline{ M}$ and $\overline{M Q}$ to create four congruent segments each with length $\frac{}{4} \mathrm{Q}$ .

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QuestionDivide the line segment $\overline{P Q}$ into four equal parts using a compass and straightedge. Choose the correct method.

Studdy Solution

STEP 1

Assumptions1. We have a line segment $\overline{ Q}$ . . We have a compass and a straight edge.
3. We want to divide $\overline{ Q}$ into four congruent segments.

STEP 2

To divide $\overline{ Q}$ into four congruent segments, we need to find the midpoint of $\overline{ Q}$ first. We can do this by constructing the perpendicular bisector of $\overline{ Q}$ .

STEP 3

STEP 4

We then draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{ Q}$ . We label the point where this line intersects $\overline{ Q}$ as $M$ .

STEP 5

Now, we have divided $\overline{ Q}$ into two congruent segments, $\overline{ M}$ and $\overline{M Q}$ .

STEP 6

We repeat the process for $\overline{ M}$ and $\overline{M Q}$ to divide them each into two congruent segments.

STEP 7

For $\overline{ M}$ , we place the point of the compass at point $$ and draw an arc that is more than half way to $M$. Without changing the compass width, we then place the point of the compass at point $M$ and draw another arc that intersects the first arc.

STEP 8

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{ M}$ . We label the point where this line intersects $\overline{ M}$ as $$.

STEP 9

We repeat the process for $\overline{M Q}$ . We place the point of the compass at point $M$ and draw an arc that is more than half way to $Q$ . Without changing the compass width, we then place the point of the compass at point $Q$ and draw another arc that intersects the first arc.

STEP 10

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{M Q}$ . We label the point where this line intersects $\overline{M Q}$ as $$.

STEP 11

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QuestionDivide the line segment PQ‾\overline{P Q}PQ​ into four equal parts using a compass and straightedge. Choose the correct method.

Studdy Solution

STEP 1

Assumptions1. We have a line segment Q‾\overline{ Q}Q​. . We have a compass and a straight edge.3. We want to divide Q‾\overline{ Q}Q​ into four congruent segments.

STEP 2

To divide Q‾\overline{ Q}Q​ into four congruent segments, we need to find the midpoint of Q‾\overline{ Q}Q​ first. We can do this by constructing the perpendicular bisector of Q‾\overline{ Q}Q​.

STEP 3

STEP 4

We then draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of Q‾\overline{ Q}Q​. We label the point where this line intersects Q‾\overline{ Q}Q​ as MMM.

STEP 5

Now, we have divided Q‾\overline{ Q}Q​ into two congruent segments, M‾\overline{ M}M and MQ‾\overline{M Q}MQ​.

STEP 6

We repeat the process for M‾\overline{ M}M and MQ‾\overline{M Q}MQ​ to divide them each into two congruent segments.

STEP 7

For M‾\overline{ M}M, we place the point of the compass at point $$ and draw an arc that is more than half way to $M$. Without changing the compass width, we then place the point of the compass at point $M$ and draw another arc that intersects the first arc.

STEP 8

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of M‾\overline{ M}M. We label the point where this line intersects M‾\overline{ M}M as $$.

STEP 9

We repeat the process for MQ‾\overline{M Q}MQ​. We place the point of the compass at point MMM and draw an arc that is more than half way to QQQ. Without changing the compass width, we then place the point of the compass at point QQQ and draw another arc that intersects the first arc.

STEP 10

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of MQ‾\overline{M Q}MQ​. We label the point where this line intersects MQ‾\overline{M Q}MQ​ as $$.

STEP 11

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QuestionDivide the line segment $\overline{P Q}$ into four equal parts using a compass and straightedge. Choose the correct method.

Assumptions1. We have a line segment $\overline{ Q}$ . . We have a compass and a straight edge.
3. We want to divide $\overline{ Q}$ into four congruent segments.

To divide $\overline{ Q}$ into four congruent segments, we need to find the midpoint of $\overline{ Q}$ first. We can do this by constructing the perpendicular bisector of $\overline{ Q}$ .

We then draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{ Q}$ . We label the point where this line intersects $\overline{ Q}$ as $M$ .

Now, we have divided $\overline{ Q}$ into two congruent segments, $\overline{ M}$ and $\overline{M Q}$ .

We repeat the process for $\overline{ M}$ and $\overline{M Q}$ to divide them each into two congruent segments.

For $\overline{ M}$ , we place the point of the compass at point $$ and draw an arc that is more than half way to $M$. Without changing the compass width, we then place the point of the compass at point $M$ and draw another arc that intersects the first arc.

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{ M}$ . We label the point where this line intersects $\overline{ M}$ as $$.

We repeat the process for $\overline{M Q}$ . We place the point of the compass at point $M$ and draw an arc that is more than half way to $Q$ . Without changing the compass width, we then place the point of the compass at point $Q$ and draw another arc that intersects the first arc.

We draw a line through the two points where the arcs intersect. This line is the perpendicular bisector of $\overline{M Q}$ . We label the point where this line intersects $\overline{M Q}$ as $$.