Question

state and prove intercept theorem ​

Answer 1

Answer:

The intercept theorem, also known as Thales' theorem (not to be confused with another theorem with the same name) or basic proportionality theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles. Traditionally it is attributed to Greek mathematician Thales.

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Answer 2

The intercept theorem, also known as Thales' theorem or basic proportionality theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles. Traditionally it is attributed to Greek mathematician Thales.

We can see that A△ACEA△CDE=ACCD (same height). Similarly, A△BCDA△CDE=BCCE.

Next, A△ADE=A△BDE (area of two triangles with the same base between parallel lines).

Hence, A△ACE=A△BCD and A△ACEA△CDE=A△BCDA△CDE

By transitivity,

ACCD=BCCE

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