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# 5.1 And 5.2 Rambo Notes

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### 5.1 And 5.2 Rambo Notes

1. 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. 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. 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. 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. 5. The trick is to READ and EXAMINE the diagram... **Know what they are looking for.... EX.
6. 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. 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. 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. 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. 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. 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. 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. 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!