math
8th Grade - Intercept Theorem

8th Grade lesson

8 - Intercept Theorem


Example

problem aubout intercept theorem

I put my hand one metre from me. With the height of my hand (5 cm), I can hide a 400 metre-high mountain standing far away. How far am I from the mountain?

If the straight lines (AD) and (BC) are parallel (it is the case here because both of them are vertical lines), then the numbers are equal. It is the Intercept theorem. The number quotient of lengths is not relevant for us here. On the contrary the equality is interesting because it gives and then with a cross product, we can find intercept theorem use, so intercept theorem use, so .


Intercept Theorem

intercept theorem
If the straight lines (FM) and (CS) are parallel then .


problem : Calculate CN in the following case knowing that (FA) and (CN) are parallel.
calculation with intercept theorem

The straight lines (FA) et (CN) are parallel, hence according to the intercept theorem, you have :
calculations with intercept theorem
intercept theorme use
intercept theorme use
intercept theorme use

The reciprocal of the intercept theorem

The reciprocal of the intercept theorem helps to prove that two straight lines are parallel if you know at least 4 lengths.
reciprocal of intercept theorem

To prove that the straight lines (XY) et (WZ) are parallel, you calculate separately the ratios then you show that at least two of them are equal :
reciprocal of intercept theorem
reciprocal of intercept theorem
reciprocal of intercept theorem so according to the reciprocal of the intercept theorem, the lines (XY) and (WZ) are parallel.



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Intercept theorem

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