Math / Geometry

QuestionSome steps to construct an angle MNT congruent to angle PQR are listed below. Step 3 is not listed:
Step 1: Draw a segment NT. Step 2: Use a compass to draw an arc from point $Q$ which intersects the side PQ of angle $P Q R$ at point $A$ and the side $Q R$ at point $B$ . Step 3: Step 4: Adjust the width of the compass to $A B$ and draw an arc from point $X$ such that it intersects the arc drawn from $N$ in a point $Y$ . Step 5: Join points $N$ and $Y$ using a straightedge. Which statement describes step 3 correctly? ( 5 points) 1) Without changing the compass width, draw an arc from point $A$ which intersects the segment NT at a point X . 2) Without changing the compass width, draw an arc from point $N$ which intersects the segment NT at a point X . 3) Without changing the compass width, draw an are from point $B$ which intersects the segment NT at a point X . 4) Without changing the compass width, draw an arc from point Twhich intersects the segment NT at a point X .

Studdy Solution

STEP 1

1. We are constructing an angle $\angle MNT$ congruent to $\angle PQR$ .
2. Steps 1, 2, 4, and 5 are given, and we need to determine the correct step 3.
3. The construction involves using a compass and straightedge.

STEP 2

1. Understand the purpose of step 3 in the context of angle construction.
2. Analyze the options provided for step 3.
3. Determine which option correctly completes the construction process.

STEP 3

Understand the purpose of step 3 in the context of angle construction:
In step 2, an arc is drawn from point $Q$ intersecting $PQ$ and $QR$ at points $A$ and $B$ . In step 3, we need to replicate this arc from point $N$ to ensure the angles are congruent.

STEP 4

Analyze the options provided for step 3:
1) Draw an arc from point $A$ . 2) Draw an arc from point $N$ . 3) Draw an arc from point $B$ . 4) Draw an arc from point $T$ .
Since the arc from $N$ should replicate the arc from $Q$ , it should intersect segment $NT$ at a point $X$ to mimic the intersection of the arc from $Q$ .

STEP 5

Determine which option correctly completes the construction process:
The correct option is: 2) Without changing the compass width, draw an arc from point $N$ which intersects the segment $NT$ at a point $X$ .
This step ensures that the arc from $N$ is congruent to the arc from $Q$ , maintaining the congruency of the angles.
The correct statement for step 3 is option 2:
$\boxed{\text{Without changing the compass width, draw an arc from point } N \text{ which intersects the segment } NT \text{ at a point } X.}$

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