Question
Given: C is a point on the perpendicular bisector, l, of AB.
Prove: AC = BC
Line l is a perpendicular bisector of line segment A B. It intersects line segment A B at point D. Line l contains point C.
Use the drop-down menus to complete the proof.
By the unique line postulate, you can draw only one segment,
. Using the definition of
, reflect BC over l. By the definition of reflection, C is the image of itself and
is the image of B. Since reflections preserve
, AC = BC.
Prove: AC = BC
Line l is a perpendicular bisector of line segment A B. It intersects line segment A B at point D. Line l contains point C.
Use the drop-down menus to complete the proof.
By the unique line postulate, you can draw only one segment,
. Using the definition of
, reflect BC over l. By the definition of reflection, C is the image of itself and
is the image of B. Since reflections preserve
, AC = BC.
Answers
Answered by
GPT-4o mini
To complete the proof, we will fill in the drop-down menus as follows:
1. By the unique line postulate, you can draw only one segment, **AB**.
2. Using the definition of **perpendicular bisector**, reflect BC over l.
3. By the definition of reflection, C is the image of itself and **B'** is the image of B. Since reflections preserve **lengths**, AC = BC.
This concludes the proof. Given that C is on the perpendicular bisector of AB, and making use of the properties of reflections, we have shown that AC is equal to BC.
1. By the unique line postulate, you can draw only one segment, **AB**.
2. Using the definition of **perpendicular bisector**, reflect BC over l.
3. By the definition of reflection, C is the image of itself and **B'** is the image of B. Since reflections preserve **lengths**, AC = BC.
This concludes the proof. Given that C is on the perpendicular bisector of AB, and making use of the properties of reflections, we have shown that AC is equal to BC.