Question

ABCD is a trapezoid with AB // CD. Its diagonals intersect in O

AB = 4; OA = 3; OB = 2; OC = 5
A) Name 2 triangles that form a Thales configuration.
B) Calculate OD and CD​

Answer 1

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Answer:

• ΔOAB ~ ΔOCD
• OD = 3 1/3; CD = 6 2/3

Explanation:

A) Thales's theorem is a theorem regarding ratios of segments when two intersecting lines cross parallel lines. It is equivalent to the theorem about side ratios in similar triangles, but there doesn't appear to be any standard meaning of "triangles that form a Thales configuration."

If the diagonals of trapezoid ABCD with parallel sides AB and CD intersect at point O, then it can be said that triangles OAB and OCD are similar.

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B) The ratios of corresponding sides are ...

OC/OA = 5/3 = OD/OB = CD/AB

Multiplying by OB, we have ...

OD = 2(5/3) = 10/3 = 3 1/3

Multiplying by AB, we have ...

CD = 4(5/3) = 20/3 = 6 2/3