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Geometry Ch5.1 #29

Question from Courtney

I’m having trouble with Chapter 5, Lesson 1, Problem 29.
I have worked the problem, I know what the answer should be, but given the figure, I don’t understand how that could be false.
Without the figure, I understand it.

Answer:

You can never assume anything. You only know what you are given in the definition. Don’t trust the figure. If it doesn’t tell you, you don’t know it. So for problem # 29 we know the following:

It’s a line
AB is less than BC
BC is less than CD
CD is less than DE

While the lengths in the figure look similar (or even equal), we don’t know that they really are similar or equal. Don’t trust anything but the defined statements in the problem and marked items in a figure.

Here is the question to think about. Given the definitions AB < BC < …. can you draw the figure such that the last DE is much larger.

Put some numbers in it and think inches.

AB = 1
BC = 2
CD = 3
DE = 500

Does that fit the definition of the problem? (Not the figure – the definition?)

Again – figures are often only ONE example that fits the problem – but they do not show every example.