1-5 Exploring Angle Pairs

Quick Review

Some pairs of angles have special names.

• Adjacent angles: coplanar angles with a common side, a common vertex, and no common interior points
• Vertical angles: sides are opposite rays
• Complementary angles: measures have a sum of 90
• Supplementary angles: measures have a sum of 180
• Linear pair: adjacent angles with noncommon sides as opposite rays

Angles of a linear pair are supplementary.

Example

Are ∠ ACE angle  and ∠ BCD angle  vertical angles? Explain.

No. They have only one set of sides with opposite rays.

Exercises

Name a pair of each of the following.

20. complementary angles
21. supplementary angles
22. vertical angles
23. linear pair

Find the value of x.

1-6 Basic Constructions

Quick Review

Construction is the process of making geometric figures using a compass and a straightedge. Four basic constructions involve congruent segments, congruent angles, and bisectors of segments and angles.

Example

Construct A B ¯ eh b bar  congruent to E F ¯ . e f bar , .

• Step 1

  Draw a ray with endpoint A.

  

• Step 2

  Open the compass to the length of E F ¯ . e f bar , .  Keep that compass setting and put the compass point on point A. Draw an arc that intersects the ray. Label the point of intersection B.

  

Exercises

26. Use a protractor to draw a 73 ° 73 degrees  angle. Then construct an angle congruent to it.
27. Use a protractor to draw a 60 ° 60 degrees  angle. Then construct the bisector of the angle.

28. Sketch L M ¯ l m bar  on paper. Construct a line segment congruent to L M ¯ . l m bar , .  Then construct the perpendicular bisector of your line segment.

    

29. 1. Sketch ∠ B angle b  on paper. Construct an angle congruent to ∠ B . angle b .

       

    2. Construct the bisector of your angle from part (a).

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