SOLUTION: Andaikan ABCD trapesium, E titik tengah kaki AD dan F titik tengah kaki BC. Buktikan bahwa EF=1/2(AB+DC)

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Question 1203590: Andaikan ABCD trapesium, E titik tengah kaki AD dan F titik tengah kaki BC. Buktikan bahwa EF=1/2(AB+DC)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Let +ABCD+be a trapezium,
+E+the midpoint of leg +AD+
+F+the midpoint of leg +BC
Prove that++EF=%281%2F2%29%28AB%2BDC%29
Capture


+ABCD is trapezium in which +AB||+DC.
+EF is parallel to side +DC.
Then we have +AB||+DC||+EF.
Hence we have also trapezium +ABFE and trapezium +EFCD.
Let +AP be the perpendicular to +DC and this intersects +EF at +Q.
+AQ will be perpendicular to +EF.
For △+APD and △+AQE+we have
+AD%2FEA=+AP%2FAQ=2
This gives +AP=2AQ+
i.e, +AQ=QP

Consider the area we have area +ABCD = area +ABFE + area +EFCD+


=>
​

=> +AP%2A%28AB%2F2%29%2BAP%2A%28+DC%2F2%29
​
=+AP%2A%28EF%2F2%29+%2BAP%2A+%28EF%2F2%29
​
=+AP%2A%28%28AB%2BDC%29%2F2%29
​
=+AP%2AEF
=>
+EF=+%28AB%2BDC%29%2F2
​

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
Google translation

Let ABCD be a trapezium, E the midpoint of leg AD and F the midpoint of leg BC. Prove that EF=1/2(AB+DC)
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I think it is proven in each and every textbook in Geometry.

Simply open, find and read.


It is a low level request to ask to "prove" what is written in every textbook.