See Problem 4.

For Exercises 16–18, draw a figure like the given one. Then construct the line through point P that is perpendicular to R S ↔ . modified r s with left right arrow above , .

B Apply

19. Think About a Plan Draw an acute angle. Construct an angle congruent to your angle so that the two angles are alternate interior angles.
    • What does a sketch of the angle look like?
    • Which construction(s) should you use?

20. Constructions Construct a square with side length p.

    

21. Writing Explain how to use the Converse of the Alternate Interior Angles Theorem to construct a line parallel to the given line through a point not on the line. (Hint: See Exercise 19.)

For Exercises 22–28, use the segments below.

22. Draw a line m. Construct a segment of length b that is perpendicular to line m.
23. Construct a rectangle with base b and height c.
24. Construct a square with sides of length a.

25. Construct a rectangle with one side of length a and a diagonal of length b.

    

26. 1. Construct a quadrilateral with a pair of parallel sides of length c.
    2. Make a Conjecture What appears to be true about the other pair of sides in the quadrilateral you constructed?
    3. Use a protractor, a ruler, or both to check the conjecture you made in part (b).
27. Construct a right triangle with legs of lengths a and b.
28. 1. Construct a triangle with sides of lengths a, b, and c.
    2. Construct the midpoint of each side of the triangle.
    3. Form a new triangle by connecting the midpoints.
    4. Make a Conjecture How do the sides of the smaller triangle and the sides of the larger triangle appear to be related?
    5. Use a protractor, ruler, or both to check the conjecture you made in part (d).
29. Constructions The diagrams below show steps for a parallel line construction.
    1. 
       Image Long Description
    2. 
    3. 
    4. 
    1. List the construction steps in the correct order.
    2. For the steps that use a compass, describe the location(s) of the compass point.

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