use only a compass and a straightedge to construct a segment congruent to CB and angle congruent to U ACB
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To construct a segment congruent to CB and an angle congruent to ∠UACB using only a compass and straightedge, follow these steps:
Step 1: Draw line segment AB, where A is the vertex of ∠UACB, and B is any point on the ray of line AC.
Step 2: Place the compass on point C and adjust its width to the length of CB. Without changing the width, draw an arc that intersects AB at point D. Label point D as the intersection of the arc and AB.
Step 3: With the same compass width, place the compass on point D and draw an arc above line AB. This arc should intersect the arc drawn in step 2 at point E.
Step 4: Using a straightedge, draw a line passing through points C and E. This line should intersect with line AB at point F.
Now, you have successfully constructed a segment CF that is congruent to CB.
To construct an angle congruent to ∠UACB using only a compass and straightedge, follow these steps:
Step 5: Place the compass on point C and adjust its width to span the segment CF. Without changing the width, draw an arc that intersects the line segment CF at two different points, G and H.
Step 6: With the same compass width, place the compass on point G and draw an arc above line CF. This arc should intersect the arc drawn in step 5 at point I.
Step 7: Using a straightedge, draw a line passing through points C and I. This line should intersect with line CF at point J.
Now, you have successfully constructed an angle ∠UCJ that is congruent to ∠UACB.
Remember, a compass is used to measure and transfer lengths, while a straightedge is used to draw straight lines. By using these tools effectively, you can construct segments and angles congruent to given ones.