# Help with this geometry/trigonometry common core question? I thought I could simply use the Pythagorean Theorem, but my teacher went over it today in class and explained that the correct answer is...

Help with this geometry/trigonometry common core question?

I thought I could simply use the Pythagorean Theorem, but my teacher went over it today in class and explained that the correct answer is something about the altitude and theorem. At this point, I was simply lost. Please help!

Thanks!

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steveschoen | Certified Educator

When your teacher was talking about the theorem, it was probably the Pythagorean Theorem.  When they were talking about the altitude, they were probably talking about one of the triangles, like base, height, and hypotenuse.

As far as this problem goes, it can be very visual.  So, it may assist if you were to separate the triangles out into the three triangles.  I have that on the attachment.

There may be several ways to do this.  The thing is, you need to show that, lack of better word, using similar triangles, you can go from something like:

ad^2 + bd^2 = ab^2      to      ab^2 + bc^2 + ac^2

Also, using the similar triangles, where ratios of sides are proportional.  We can write:

ac          ab

Multiplying each side by "ab", we get:

ac

Similarly, using similar triangles, we can write:

bc    =   bd
ac         ab

Multiplying each side by "ab", we get:

bd = ab*bc
ac

Substituting these into our initial Pythagoream Theorem, "ad^2 + bd^2 = ab^2", we get:

(ab^2)^2  +  (ab*bc)^2   =   ab^2
ac^2             ac^2

ab^4   +   ab^2*bc^2   =   ab^2
ac^2              ac^2

Multiplying each side by "ac^2", we get:

ab^4  +  ab^2*bc^2   =   ab^2*ac^2

Dividing each side by "ab^2", we get:

ab^4  +  ab^2*bc^2   =   ab^2*ac^2
ab^2           ab^2                ab^2

Cancelling out ab^2 on the left side, we get:

ab^2 + bc^2 = ac^2

Which is what the question is asking you to prove.

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kseddy123 | Student

Plz check this answer this is very simple to understand hope this helps you

plz check the attachments for the clear answer

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