Question 835300: I have no idea how to post an image, but I was able to find an exact image on another persons question, see link below.
I know how to do the work, I just am unsure as to which definition (theorems) goes where, which is the only part I need help in identifying. This is what I have so far....
Line 1 is triangle ABC, AD bisects angle BAC and AE are ~(with equal sign)ED Reason is given
Line 2 is angle BAD = angle EAD with the reason AD intersects angle BAC
Line 3 AE = ED reason: similar sides are equal
Line 4 angle ADE = EAD reason property of isosceles triangles
Line 5 angle BAD = ADE Reason: angle BAD and angle ADE = angle EAD
Line 6 AB is parallel to ED Reason: lines are considered parallel
Line 7 angle CDE is congruent to angle CBA and CED is congruent to angle CAB Reason: angle will be congruent to each other if two parallel lines are divided by a transversal angle
Line 8 Angle DCE is congruent to angle BCA Reason AAA postulate
Line 9 1). AC/EC= BC/DC reason: conforming sides are directly in proportion to congruent triangles
Line 10 DC Reason subtract 1 on both sides 1).
Line 11 3). AE/EC = BD/DC Reason simplified line 10
Line 12 AE/AC = BD/BC Reason 3). divided by 2).
link to image http://www.algebra.com/algebra/homework/Geometry_proofs.faq.question.630966.html
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
Given: ΔABC, AD bisects ∠BAC, AE ≅ ED
To prove: AE/AC = BD/BC
1 In ΔABC, AD bisects ∠BAC and AE ≅ ED ---- given
2 m∠BAD = m∠EAD ------- AD bisects ∠BAC
3 ΔAED is isoceles ------- AE ≅ ED, which is given
4 m∠EAD + m∠ADE + m∠AED = 180° ------ property of all triangles
5 m∠ADE = m∠EAD ------- property of isosceles ΔAED
6 m∠BAD + m∠EAD + m∠AED = 180° ------ substituting =s for =s (2 and 5)
7 ∠BAC = ∠BAD + ∠EAD ------- a whole is equal to the sum of its parts.
8. m∠BAC = m∠BAD + m∠EAD ------- measure of whole equals sum of measures of parts
9. m∠BAC + m∠AED = 180° -------- substituting =s for =s (6 and 8)
10. AB ∥ ED -------- if two interior angles on the same
side of a transversal cutting two
lines are supplementary then the
lines are parallel"
11 AE/EC = BD/DC -------- If a line parallel to a side of a triangle
intersects the other two sides, then it
divides those sides proportionally.
12 AE/(EC+AE) = BD/(DC+BD) -------- Numerator addition property of a
proportion.
13 AE/AC = BD/BC -------- AC = EC+AE and BD = DC+BD,
substituting =s for =s
Edwin
|
|
|
