5.1 And 5.2 Rambo Notes

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  • 1. 5.1 Polygon Sum Conjecture pg. 256 to 259 Warm Up: pg. 259 # 18, pg. 263 # 15, 16 R D 18. x=120° 15. Yes, ΔRAC≅ΔDCA by SAS A AD≅CR by CPCTC C 16. Yes. ΔDAT≅ΔRAT by SSS D <D≅<R by CPCTC A T R
  • 2. Pg. 256 Investigation-- No. of polygon sides 3 4 5 6 7 8 .... n Sum of angle meas. 180° 360° 540° 720° 900° 1080° .... 180°(n-2) What does this mean??? --You can either MEMORIZE all the degrees for EVERY SHAPE EVER or you can use the formula 180°(n-2) (used to find the SUM of the ANGLES of ANY POLYGON) 180° --sum of angles in triangle (n-2) represents # of Δ's in the polygon when divided by diagonals from ONE vertex
  • 3. 5.2 Exterior Angles of Polygons Sum of Exterior Angles Answer is ALWAYS 360° That is the ONLY answer, EVER!!!!! Why?? if you take ALL of the verticies of ANY polygon and pull them into the center of that polygon--it forms a CIRCLE EACH Interior Angle measure ONLY works with regular polygon because all the angles are equal!!! Uses the Polygon Sum formula and then divides by the number of angles--same as the number of sides!!!! 180° (n-2) n
  • 4. TO Summarize Sections 5.1 and 5.2...: Formula for: 180° (n - 2) Each interior angle: n Sum of exterior Angles: 360° Each exterior angle: 360° n Sum of Interior angles: 180° (n - 2)
  • 5. The trick is to READ and EXAMINE the diagram... **Know what they are looking for.... EX.
  • 6. EXAMINE the diagram... 1st... How many sides? 7 (so that means n=7) 2nd...Use the SUM of interior angles formula 180°(n-2) Substitute 7 for n and do the math... Sum for a heptagon is 900° 3rd... Subtract all the angles from 900° to get answer...145°
  • 7. What if they want EACH interior angle of a polygon? READ and EXAMNIE picture.... What is the measure of an interior angle in a regular pentagon? *What is n? =--- 5 *What formula=---- 180°( n - 2)/ n Substitute 5 for n... 180°( 5 -2) / 5 = 108° Why this one? BECASUE they want "an" angle not the SUM THIS ONLY WORKS ON REGULAR POLYGONS!!!!
  • 8. Sometimes they give you this.... Find each interior angle measure of this regular polygon Ask yourself.. What is it? Pentagon (5 sides so n = 5) USE formula for EACH interior angle: 180°(n-2)/n substitute and solve!
  • 9. Exterior Angle Sum: How does that work???? Think!--If the shape sucks itself into the center, what are you left with? Right!--A circle which is 360° DOESN"T matter which polygon--ALL polygons have EXTERIOR ANGLE SUMS of 360°
  • 10. Try it... 1. What is the sum of the measures of the exterior angles of a pentagon? 360° 2. The sum of the measures of the exterior angles of a 30-gon is___360°__ 3. b a d c what is the sum of the lettered angles? 360°
  • 11. Lastly if the SUM of the exterior angles of a polygon is 360°.... How do you get EACH exterior angle of a polygon? 1. It HAS to be a regular polygon! Other wise this will not work! 2. Take the sum 360° and divde by the number of sides! 360°/n
  • 12. Example..... What is the measure of each exterior angle of a regular hexagon? 1. Identify n! (6) 2. Plug in 360°/ 6 3. Solve.. 60° the words tell you what formula to use
  • 13. Try these videos...... Polygon sum formula http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037878-X/Ch03/03-04/PH_Geom_ch03- 04_Obj2_vid1.html Exterior Angle Sum Try the Dynamic exploration on Textbook link!