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Magazine Chapter 5: Q1 (page 179)
You can use a sheet of lined notebook paper to divide a segment into a number of congruent parts. Here a piece of cardboard with edge is placed so that is separated into five congruent parts. Explain why it works.
Short Answer
The cardboard with edge can be divided into five congruent parts using a sheet of lined notebook paper.
Step by step solution
Step 1. Consider the diagram.
Here, has to be separated into five congruent parts.
Step 2. State the explanation.
Using the given fact, edge of the notebook will cut off equal transversal on the parallel lines k, l and m of the notebook paper. That is,
.
From similar arguments for the lines l, m and n.
.
From similar arguments for the lines m, n and o.
.
From similar arguments for the lines n, oand p.
From the definition, equal segments are congruent.
Therefore, the above argument is divided into 5 congruent parts.
Step 3. State the conclusion.
Therefore, from the above facts, equal segments are congruent proves that is divided into 5 congruent parts.
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