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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 44 Page 580

Recall that if three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

See solution.

Practice makes perfect

Let's begin with recalling what we can say about congruent parts of parallel lines using the Three Parallel Lines Theorem.

Three Parallel Lines Theorem
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Having this information in mind, let's construct a segment separated into five congruent segments. We will start with drawing a segment AB.

Next, we will draw the second segment AC.

After this, with the compass at A, we will mark off an arc that intersects AC at X.

Using the same compass setting we will mark off Y,Z,W and Q such that AX≅XY≅YZ≅ZW≅ WQ.

The next step will be to connect B and Q with a segment.

Finally, we will construct lines through X,Y,Z and W that are parallel to QB. Label the intersection points on AB as J,K,L and M.

Since parallel lines cut off congruent segment on transversals, AJ≅JK≅KL≅LM≅MB. Finally, we separated segment AB into five congruent segments.

Subchapter links

Exercises p.577-581