Math Is Fun Forum

Neha

Member

Registered: 2006-10-11

Posts: 173

Given

B                       E                       C
-----------------------------------------
|                       /\                       |
|                     /    \                     |
|                   /        \                   |
|                 /            \                 |
|               /                \               |
|             /                    \             |
|           /                        \           |
|         /                            \         |
|       /                                \       |
|     /                                    \     |
|   /                                        \   |
| /                                            \ |
-----------------------------------------
A                                                 D

given : ABCD is a rectangle ; E is the midpoint of BC.
write a proof to show that:
     ~   
AE = DE

given statements and reasons to those statements

HELP:/

---

Live Love Life

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Given

First prove that triangle ABE and EDC are similar through SAS (you have to find which sides and which angle though).

Then, prove that they are congruent, which is pretty much the equivalent of stating BE = EC.

Then state that this means...

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Given

If you can show SAS, then you've already shown congruence. And then it's a simple matter to say that AE and DE are sides of 2 congruent triangles and therefore are equal.

---

Why did the vector cross the road?
It wanted to be normal.