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Special Pairs of Angles Lesson 2.4 Geometry Honors

Special Pairs of Angles Lesson 2.4 Geometry Honors. Objective: Apply the definitions of complementary and supplementary angles. State and apply the theorem about vertical angles. Page 50. Lesson Focus.

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Special Pairs of Angles Lesson 2.4 Geometry Honors

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  1. Special Pairs of AnglesLesson 2.4Geometry Honors Objective: Apply the definitions of complementary and supplementary angles. State and apply the theorem about vertical angles. Page 50

  2. Lesson Focus Pairs of angles whose measures have the sum of 90 or 180 appear frequently in geometric situations. For this reason, they are given special names. This lesson studies these special angles and solves problems involving them.

  3. Special Pairs of Angles Complementary angles (comp. s) Two angles whose measures have the sum 90. Each angle is called the complement of the other. Example: Given: 1 and 2 are complements. If m1 = 42, then m2 = 48.

  4. Special Pairs of Angles Supplementary angles (supp. s) Two angles whose measures have the sum of 180. Each angle is called the supplement of the other. Example: Given: 1 and 2 are supplements. If m1 = 109, then m2 = 71.

  5. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. Because 32°+ 58° = 90°, BACand RSTare complementary angles. Because 122° + 58° = 180°,CADand RSTare supplementary angles. Because BACand CADshare a common vertex and side, theyare adjacent. EXAMPLE 1 Identify complements and supplements SOLUTION

  6. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. 1. Because 41° + 49° = 90°, FGK and GKLare complementary angles. Because 49° + 131° = 180°,HGKand GKL are supplementary angles. Because FGKand HGKshare a common vertex and side, theyare adjacent. for Example 1 GUIDED PRACTICE

  7. Special Pairs of Angles Vertical Angles (Vert. s) Two angles such that the sides of one angle are opposite rays to the other sides of the other angle. When two lines intersect, they form two pairs of vertical angles.

  8. Special Pairs of Angles Vertical Angle Theorem Vertical angles are congruent. Proof: 1 and 2 form a linear pair, so by the Definition of Supplementary Angles, they are supplementary. That is, m1 + m2 = 180°. (also, Angle Addition Postulate) 2 and 3 form a linear pair also, so m2 + m3 = 180°. Subtracting m2 from both sides of both equations, we get m1 = 180° − m2 = m3. Therefore, 1  3. You can use a similar argument to prove that 2  4.

  9. Sports When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find mBCEand mECD. EXAMPLE 3 Find angle measures

  10. Practice Quiz Complete with always, sometimes, or never. • Vertical angles _____ have a common vertex. • Two right angles are _____ complementary. • Right angles are _____ vertical angles. • Angles A, B, and C are _____ complementary. • Vertical angles _____ have a common supplement.

  11. Practice Quiz Complete with always, sometimes, or never. • Vertical angles always have a common vertex. • Two right angles are never complementary. • Right angles are sometimes vertical angles. • Angles A, B, and C are never complementary. • Vertical angles always have a common supplement.

  12. Homework Assignment Page 53 – 54 Problems 19 – 31 odd, 32 – 35.

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