Practice and Problem-Solving Exercises

A Practice

See Problem 1.

For Exercises 7–14, draw a diagram similar to the given one. Then do the construction. Check your work with a ruler or a protractor.

7. Construct X Y ¯ x y bar  congruent to A B ¯ . eh b bar , .

   

8. Construct V W ¯ v w bar  so that V W = 2 A B . v w equals 2 eh b .
9. Construct D E ¯ d e bar  so that D E = T R + P S . d e equals t r plus p s .

   

10. Construct Q J ¯ q j bar  so that Q J = T R − P S . q j equals t r minus p s .

See Problem 2.

11. Construct ∠ D angle d  so that ∠ D ≅ ∠ C . angle d approximately equal to angle c .

    

12. Construct ∠ F angle f  so that m ∠ F = 2 m ∠ C . m angle , f equals 2 m , angle c .

See Problem 3.

13. Construct the perpendicular bisector of A B ¯ . eh b bar , .

14. Construct the perpendicular bisector of T R ¯ . t r bar , .

See Problem 4.

15. Draw acute ∠ PQR . angle  Then construct its bisector.
16. Draw obtuse ∠ XQZ . angle  Then construct its bisector.

B Apply

Sketch the figure described. Explain how to construct it. Then do the construction.

17. X Y ↔ ⊥ Y Z ↔ modified x y with left right arrow above , up tack , modified y z with left right arrow above
18. S T → s t vector  bisects right ∠ PSQ . angle
19. Compare and Contrast How is constructing an angle bisector similar to constructing a perpendicular bisector?

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