1-3 Measuring Segments

Quick Review

The distance between two points is the length of the segment connecting those points. Segments with the same length are congruent segments. A midpoint of a segment divides the segment into two congruent segments.

Example

Are A B ¯ eh b bar  and C D ¯ c d bar  congruent?

A B = | − 3 − 2 | = | − 5 | = 5 eh b equals vertical line negative 3 minus 2 vertical line equals vertical line negative 5 vertical line equals 5

C D = | − 7 − ( − 2 ) | = | − 5 | = 5 c d equals vertical line negative 7 minus open negative 2 close vertical line , equals vertical line , minus 5 vertical line equals 5

A B = C D , eh b equals c d comma  so A B ¯ ≅ C D ¯ . eh b bar , approximately equal to , c d bar , .

Exercises

For Exercises 12 and 13, use the number line below.

12. Find two possible coordinates of Q such that P Q = 5 . p q equals 5 .

13. Use the number line above. Find the coordinate of the midpoint of P H ¯ . p h bar , .

    

14. Find the value of m.

    

15. If X Z = 50 , x z equals 50 comma  what are XY and YZ?

    

1-4 Measuring Angles

Quick Review

Two rays with the same endpoint form an angle. The endpoint is the vertex of the angle. You can classify angles as acute, right, obtuse, or straight. Angles with the same measure are congruent angles.

Example

If m ∠ AOB = 47 bold italic m angle  and m ∠ BOC = 73 , bold italic m angle  find m ∠ AOC . bold italic m angle

m ∠ AOC = m ∠ AOB + m ∠ BOC   = 47 + 73   = 120 table with 3 rows and 2 columns , row1 column 1 , m angle

Exercises

Classify each angle as acute, right, obtuse, or straight.

Use the diagram below for Exercises 18 and 19.

18. If m ∠ MQR = 61 m angle  and m ∠ MQP = 25 , m angle  find m ∠ PQR . m angle
19. If m ∠ NQM = 2 x + 8 m angle  and m ∠ PQR = x + 22 , m angle  find the value of x.

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