##### Question Group Info

This question group is public and is used in 5 tests.

Author: nsharp1
No. Questions: 3
Created: Nov 6, 2018

# Points on perpendicular bisector proof

## View group questions.

To print this group, add it to a test.

Given line segment $bar{AC}$ with midpoint $B$ and perpendicular bisector $l$ (not pictured), which intersects $bar{AC}$ at $B$, prove that any point on line $l$ is equidistant from points $A$ and $C$.

 $" Statement "$ $" Reason "$ $1. "Let " P " be an arbitrary point on line "$ $\ \ \ \ \ l " that does not lie on "bar{AC}$ $1. "A line consists of an infinite number of points"$ $2. "Construct "bar{AP}" and "bar{CP}$ $2. "Two points define a line segment"$ $3.$ $3. "Reflexive property"$ $4. B " is the midpoint of " bar{AC}$ $4. "Given"$ $5. bar{AB} ~= bar{BC}$ $5. "Definition of midpoint"$ $6. l " is the perpendicular bisector of " bar{AC}$ $6. "Given"$ $7. ang ABP " and " ang PBC " are right angles"$ $7. "Definition of perpendicular"$ $8. ang ABP ~= ang PBC$ $8. "All right angles are congruent"$ $9. Delta ABP ~= Delta CBP$ $9. ""$ $10. bar{AP} ~= bar{PC}$ $10. "Corresponding sides of congruent triangles "$ $\ \ \ \ " are congruent"$ $11. P " is equidistant from " A " and " C$ $11. "Definition of equidistant"$
Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9
A.
What is the missing statement in step 3?
1. $l ~= l$
2. $bar{BP} ~= bar{BP$
3. $bar{AB} ~= bar{BC}$
4. $bar{AC} ~= bar{AC}$
Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9
Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9
C.
What still needs to be done in order to complete the proof?
1. Consider other points on $l$, showing the same thing holds true for these other points.
2. Redraw the diagram, showing that the results are still true if $l$ is horizontal and $bar{AC}$ is vertical.
3. State that, if the point on $l$ lies on $bar{AC}$, that it is equidistant from points $A$ and $B$, due to $l$ bisecting $bar{AC}$ (from given information).
4. Nothing, it is complete.