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Geometry Agenda

This geometry agenda covers warm-up exercises, notes on triangle angles, and practice problems. Learn about interior and exterior angles, the Base Angles Theorem, and the Exterior Angle Theorem.

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Geometry Agenda

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  1. Geometry Agenda • Warm up • Mapquest 2 • Interior/Exterior Triangle Angles • Notes • Practice

  2. Begin at the word “Today”. Every Time you move, write down the word(s) upon which you land. is Show Spirit! Session 5 Warm-up 1. Move to the corresponding angle. homecoming! 2. Move to the vertical angle. Today 3. Move to the supplementary angle. 4. Move to the alternate interior angle. . 5. Move to the vertical angle school your 6. Move to the alternate exterior angle. GO JAGS! 7. Move to the consecutive exterior angle.

  3. MAPQUEST 2

  4. CCGPS Analytic Geometry UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms? Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13 Today’s Question: If the legs of an isosceles triangle are congruent, what do we know about the angles opposite them? Standard: MCC9-12.G.CO.10

  5. Triangles & Angles September 27, 2013

  6. Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. If , then

  7. Converse of Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. If , then

  8. EXAMPLE 1 Apply the Base Angles Theorem Find the measures of the angles. SOLUTION Q P Since a triangle has 180°, 180 – 30 = 150° for the other two angles. Since the opposite sides are congruent, angles Q and P must be congruent. 150/2 = 75° each. (30)° R

  9. EXAMPLE 2 Apply the Base Angles Theorem Find the measures of the angles. Q P (48)° R

  10. EXAMPLE 3 Apply the Base Angles Theorem Find the measures of the angles. Q P (62)° R

  11. EXAMPLE 4 Apply the Base Angles Theorem Find the value of x. Then find the measure of each angle. P SOLUTION (12x+20)° Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 12x + 20 = 20x – 4 20 = 8x – 4 24 = 8x 3 = x (20x-4)° Q R Plugging back in, And since there must be 180 degrees in the triangle,

  12. Right Triangles HYPOTENUSE LEG LEG

  13. Exterior Angles Interior Angles

  14. Triangle Sum Theorem The measures of the three interior angles in a triangle add up to be 180º. x + y + z = 180° x° y° z°

  15. R m R + m S + m T = 180º 54° 54º + 67º + m T = 180º 121º + m T = 180º 67° S T m T = 59º

  16. m  D + m DCE + m E = 180º E 55º + 85º + y = 180º B y° 140º + y = 180º C x° 85° y = 40º 55° D A

  17. Find the value of each variable. x° 43° x° 57° x = 50º

  18. Find the value of each variable. 55° 43° (6x – 7)° (40 + y)° 28° x = 22º y = 57º

  19. Find the value of each variable. 50° 53° 50° 62° x° x = 103º

  20. Exterior Angle Theorem The measure of the exterior angle is equal to the sum of two nonadjacent interior angles 1 m1+m2 =m3 2 3

  21. Ex. 1: Find x. B. A. 72 43 148 76 x x 38 81

  22. Homework: Practice WS

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