In figure A and B are on the same side of line L. AD perpendicular to l and BE perpendicular to l. If C is the midpoint of AB proove that CD = CE.
There is a lot of missing information here. I can easily devise a scenario where the assertion is false.
Suppose A is 1 cm above L and B is 10 cm above L.
If D and E are on L, clearly CD < CE.
Ac equal to bc(midpoint)
Draw cm that is median
Triangle cdm is congruent to triangle CME
That is cd epual to ce(cpct)
To prove that CD = CE, we can use the properties of a perpendicular bisector and the fact that C is the midpoint of AB.
Here's how you can go about proving it step by step:
1. Draw the given figure with line L and points A, B, C, D, E as described in the question.
2. Since AD is perpendicular to line L and BC is perpendicular to line L, we have two pairs of congruent right triangles: ACD and BCE (By definition of perpendicular lines).
3. Now, observe that AC = BC (By definition of midpoint).
4. Using congruent right triangles ACD and BCE, we can conclude that CD = CE (By HL- Hypotenuse Leg Congruence Theorem).
Therefore, we have proved that CD = CE using the given information.