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Question 1041084: Use the following image to answer the questions below.
https://byuis.brainhoney.com/Resource/46824920,0/Assets/Media/Images/41.2-HOT2-Angle.jpg
a. Based on the picture, what properties can you be sure this figure has? Think about angles, lines, and points.
b. Does line l $ bisect angle ABC? Explain your thinking.
c. What would you need to do to prove that line l bisects angle ABC?
WHAT I WROTE:
a) Right angle (angle ABC), points (point A, B, C ,D), line segments (segment AB, segment BC, segment BD), ray (ray BD), angles (angle DBC, angle ABD)
b) Yes, line l does bisect angle ABC because it splits angle ABC into two equal halves at 45 degrees each.
c) You would need to know the angle bisector (l) and the midpoint (B).
Thanks in advance!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
1. Wrong. There is absolutely nothing other than your intuition that tells you angle ABC is a right angle. Yes, indeed, it looks like a right angle, but it might very well be an 89.999 degree angle and you would not be able to tell the difference and yet that would make your statement that BD is a bisector of angle ABC a completely false assertion.
2. Wrong. Same reason.
3. Wrong. "Knowing the bisector (1)" is meaningless (where did you meet it? at a cocktail party?), B is not the midpoint of anything, except perhaps an extended segment from A, C, or D through B to a point equidistant, and that would have absolutely nothing to do with proving that BD is a bisector of ABC. You would have to know that the measure of angle ABD is 45 degrees or that the measure of angle ABC is 90 degrees or that angle ABC is a right angle.
John
My calculator said it, I believe it, that settles it
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