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Question 1181239: On square ABCD, E is the midpoint of side AB.
Diagonal AC intersects segment ED at X. Find the
length of segment EX if AB 6cm.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Draw a sketch of the figure.
DE and AC are transversals that cut parallel segments AB and CD, so the angles of triangle AXE are congruent to the angles of triangle CXD.
That makes triangles AXE and CXD similar; since AE=3 and CD=6, the ratio of similarity is 1:2.
That means the ratio of EX to DX is 1:2; and that means EX is 1/3 of DE.
Use the Pythagorean Theorem on triangle ADE to find the length of DE and thus find the length of EX.
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