Question 1136840: Can someone help me solve this problem? here goes and here's the figure:
https://i.imgur.com/aMC2jMX.png
A landscaper designed a garden. The landscaper has decided to place point B 22 feet east of point A, point C 44 feet east of point A, point E 36 feet south of point A, and point D 36 feet south of point C. The angles at points A
and C are right angles. Prove that angle ABE is congruent to CBD.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
We are given that "The landscaper has decided to place point B 22 feet east of point A", so segment AB is 22 feet long. Also we're told that "point C 44 feet east of point A" meaning AC = 44 feet, so BC = AC - AB = 44 - 22 = 22; therefore, AB and BC are both 22 feet long. Making AB = BC a true statement.
The two facts "point E 36 feet south of point A, and point D 36 feet south of point C" tell us that AE = 36 and CD = 36, so both of these are the same length, ie AE = CD.
The information that "The angles at points A and C are right angles" tells us we have two right triangles. The angles at points A and C are 90 degrees each.
We use the SAS (side angle side) congruence theorem to prove that the triangles are congruent to one another. Note how the congruent angles (A and C) are between the two pairs of congruent sides AB = BC and AE = CD
The last step is to use CPCTC (corrsponding parts of congruent triangles are congruent) to conclude that angle ABE = angle CBD
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