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PROVING ANGLES CONGRUENT

PROVING ANGLES CONGRUENT. Vertical angles Two angles whose sides form two pairs of opposite rays. 1. 4. 3. 2. The opposite angles in vertical angles are congruent. In this case angles 1 & 2 would be congruent and angles 3 & 4 would be congruent.

joan-gross
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PROVING ANGLES CONGRUENT

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  1. PROVING ANGLES CONGRUENT

  2. Vertical angles Two angles whose sides form two pairs of opposite rays 1 4 3 2 The opposite angles in vertical angles are congruent. In this case angles 1 & 2 would be congruent and angles 3 & 4 would be congruent.

  3. Because angles 1 & 4 form a straight line as well as angles 3 & 2 we only have to know the measure of one angle to know all of the angle 200 1 4 600 3 600 2 1200 If angle 3 is 600, then angle 2 would be 1200 because they make a straight angle of 1800. Then angle 4 would be 600 being vertical to angle 3 and angle 1 would be 1200 being vertical to angle 2

  4. Adjacent angles Two coplanar angles with a common side, a common vertex, and no common interior points In other words, two angles share one of the same rays

  5. Complementary angles Two angles whose measures have the sum of 900 Each angle is called the complement of the other 400 500 As you can see from the figures the two angles can be adjacent or they can be separated but the angles must add up to 900

  6. Supplementary angles Two angles whose measures have the sum of 1800 Each angle is called the supplement of the other Here again, they can be adjacent or they may be two separate angles but their measure will be 1800 1050 750

  7. Identifying Angle Pairs Name a set of complementary angles < 2 and < 3 A set of supplementary angles < 4 and < 5 < 3 and < 4 Vertical angles < 3 and < 5 2 1 3 5 4

  8. F A E B D C Name the adjacent angles: If m<EFD = 27, what is the m<AFD 180 – 27 = 153

  9. F A E B D C Conclusions you can draw from the diagram Adjacent angles Adjacent supplementary angles Vertical angles

  10. Things you cannot assume F A E B D C Angles or segments that are congruent If an angle is a right angle Lines are parallel or perpendicular We can assume these if there are markings

  11. What can you conclude from this diagram? <1 and <2 Congruent <2 and <3 Adjacent <4 and <5 adjacent supplementary angles <1 and <4 vertical angles 2 4 3 5 1 What conclusions can you make here? T Q P W V

  12. Assignment Page 100 1 – 18 20 – 22 29 – 30 32 - 34

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