Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the length of each segment.

8. A B ¯ eh b bar
9. B D ¯ b d bar
10. A D ¯ eh d bar
11. C E ¯ c e bar

See Problem 2.

Use the number line below for Exercises 12–14.

12. If R S = 15 r s equals 15  and S T = 9 , s t equals 9 comma  then R T = □ . r t equals white square .
13. If S T = 15 s t equals 15  and R T = 40 , r t equals 40 comma  then R S = □ . r s equals white square .
14. Algebra R S = 8 y + 4 , S T = 4 y + 8 , r s equals 8 y plus 4 comma s t equals 4 y plus 8 comma  and R T = 15 y − 9 . r t equals 15 y minus 9 .
    1. What is the value of y?
    2. Find RS, ST, and RT.

See Problem 3.

Use the number line below for Exercises 15–18. Tell whether the segments are congruent.

15. L N ¯ l n bar  and M Q ¯ m q bar
16. M P ¯ m p bar  and N Q ¯ n q bar
17. M N ¯ m n bar  and P Q ¯ p q bar
18. L P ¯ l p bar  and M Q ¯ m q bar

See Problem 4.

19. Algebra A is the midpoint of X Y ¯ . x y bar , .

    

    1. Find XA.
    2. Find AY and XY.

Algebra For Exercises 20–22, use the figure below. Find the value of PT.

20. P T = 5 x + 3 p t equals 5 x plus 3  and T Q = 7 x − 9 t q equals 7 x minus 9
21. P T = 4 x − 6 p t equals 4 x minus 6  and T Q = 3 x + 4 t q equals 3 x plus 4
22. P T = 7 x − 24 p t equals 7 x minus 24  and T Q = 6 x − 2 t q equals 6 x minus 2

B Apply

On a number line, the coordinates of X, Y, Z, and W are − 7 , − 3 , 1 , negative 7 comma negative 3 comma 1 comma  and 5, respectively. Find the lengths of the two segments. Then tell whether they are congruent.

23. X Y ¯ x y bar  and Z W ¯ z w bar
24. Z X ¯ z x bar  and W Y ¯ w y bar
25. Y Z ¯ y z bar  and X W ¯ x w bar

Suppose the coordinate of A is 0, A R = 5 , eh r equals 5 , comma  and A T = 7 . eh t equals 7 .  What are the possible coordinates of the midpoint of the given segment?

26. A R ¯ eh r bar
27. A T ¯ eh t bar
28. R T ¯ r t bar
29. Suppose point E has a coordinate of 3 and E G = 5 . e g equals 5 .  What are the possible coordinates of point G?

Table of Contents