Definition of perpendicular proof

Asked by maham237 @ 05/01/2021 in Mathematics viewed by 174 People

iven: C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC 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.

Answered by maham237 @ 05/01/2021

Answer:

See the attached figure for better explanation :

Step-by-step explanation :

1. By the unique line postulate, you can draw only one line segment : BC

Since only one line can be drawn between two distinct points.

2. Using the definition of reflection, reflect BC over l.

To find line segment which reflects BC over l, we will use the definition of reflection.

3. By the definition of reflection, C is the image of itself and A is the image of B.

Definition of reflection says the figure about a line is transformed to form the mirror image. Now, CD is perpendicular bisector of AB so A and B are equidistant from D forming the mirror image of each other.

4. Since reflections preserve length, AC = BC

In Reflection the figure is transformed to form a mirror image, Hence the length will be preserved in case of reflection.

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