EX 1 Find the length of each side EX 2 Find the value of a, b, c, d. if the perimeter is 20.

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1 HOW DOES THIS APPLY? EX Fid the legth of eh side EX 2 Fid the vlue of, b,, d. if the perieter is 20. To solve or ot to solve? C you solve usig properties of isoseles trigles disovered? If so, write the property used. Wht is the esure of the vertex gle of LMN if 2x 6 d 2 x 3? XYW is isoseles trigle. WY is 0 etieters log. Fid the legth of XZ.

2 If the perieter of the equilterl trigle show below is 37 etieters, wht is the pproxite re of the trigle? A trigle is isribed i squre, s show below. Wht is the re of the shded trigle isribed i the squre? Mr. Shultz hs grde shped lie equilterl trigle tht esures feet o eh side. He hs pled wterig hose tht exteds fro the fuet loted t vertex to the opposite side, s show below? Wht is the legth of the hose i the grde?

3 Notes: Agles i Trigles d Polygos Geoetry setios 3-4 d 3-5 Ne: Dte: Period: Agles i Trigles: 2, 4, d 6 re iterior gles , 3, d 5 re exterior gles Agles i Polygos: iterior gle exterior gle Trigle Agle-Su Theore: The su of esures of the iterior gles of trigle is. Write this theore s equtio, usig the gles i the digr bove: = Pi gle esure for 6 (ot 60!) d differet gle esure for 4. Lbel the i the digr bove. Wht ust be the esure of 2? Let s loo t the reltioship betwee the iterior d exterior gles of trigle: 5 is exterior gle. Sie 5 d 6 re lier pir, 5 =. Lbel it i the digr. 5 hs two reote iterior gles: 2 d 4. Wht is the reltioship betwee the esures of 5, 2, d 4? Write it s equtio: = +. Is this is true for the other exterior gles? 3 = +. = +. Trigle Exterior Agle Theore: The esure of eh exterior gle of trigle equls the of its two gles. Polygos Not Polygos Qulities Polygos hve i oo: Qulities No-Polygos hve i Coo: Wht is polygo? Now tht we ow wht geeri polygo is, let s loo t speil group of polygos, the regulr polygos. Here re few regulr polygos: Equilterl Squre Regulr Regulr Regulr Trigle Petgo Hexgo Otgo A equilterl polygo hs ll ogruet. A equigulr polygo hs ll ogruet. A regulr polygo is both d.

4 3-5 Prtie Probles: Ne: Fid the su of the esures of the iterior gles of eh polygo.. -go go 3. dego Wht would be the esure of oe gle i regulr polygo with eh of these ubers of sides? (Reeber, ll gles i regulr polygo re the se) 4. 5-go su of gle esures go su of gle esures oe gle oe gle The esure of oe exterior gle i regulr polygo is give. Fid the uber of sides i the polygo. Ex. 60 degrees: 360 = 6 sides degrees degrees degrees Ne the polygo Let s fid the esure of eh gle i this petgo. First we eed to ow wht we will get whe we dd up ll the gles: Now we just dd ll of the gles together d set the equl to this uber. After we fid y, we plug it i for eh idividul gle. B y = A 2y-5 A = 20 B = C = 2y D = 3y-25 C E E = 2y Additiol Exerises: p6 # 2, 25, 33, 4, 47. D 2. Fid the issig gle esures i the figure o the right. = ( + 6) = 25. A regulr 00-go hs iterior gle of degrees d exterior gle of degrees. 33. A polygo with sides hs gles whose esures su to 080. Fid. 4. A regulr polygo hs exterior gle of 36. Its iterior gle is degrees. The uber of sides is. 47. y = z = This polygo is lled.

5 Rottios Fill i the rows for "Rottios" i the Uit Fous hrt. Is it isoetry? Turig or spiig figure o the ple is lled. I this ourse, ll rottios will be lowise or outerlowise? (Cirle oe) I the figure to the right, the degree of rottio is the esure of gle. The eter of rottio is. Uder 90 rottio, figure i Qudrt I would be pped to Qudrt. The ppig ottio for 90 rottio is. Uder 80 rottio, figure i Qudrt I would be pped to Qudrt. The ppig ottio for 80 rottio is. G H I Uder 270 rottio, figure i Qudrt I would be pped to Qudrt. The ppig ottio for 270 rottio is. Uder 360 rottio, figure i Qudrt I would be pped to Qudrt. Aother wy reeber the ptter: For eh 90 of rottio, swith the d oordites; the deterie the or sigs bsed o the qudrt fter rottio. Fid the ige of E (-4, ) fter 90 rottio. Fid the ige of J (-2, -3) fter 80 rottio. Fid the ige of K (3, 0) fter 270 rottio. Wht is the slope of EJ? Wht will be slope be fter 90 rottio? 80 rottio? 270 rottio? Syetry If there is isoetry or trsfortio tht ps the figure oto itself, the the figure hs. Syetry: There is refletio tht ps the figure oto itself. Lie syetry (hs oe or ore lies of refletio) Syetry: There is rottio of 80 or less tht ps the figure oto itself. The gle of rottio is the sllest gle eeded for the figure to rotte o itself. Poit Syetry: the figure hs 80 rottiol syetry. If there is refletiol syetry, seth the lie(s) of syetry: How y lies of syetry? Is there rottiol syetry? If yes, wht is the gle of rottio? 5 turs for oe revolutio 360 /5 = Whih figure(s) hve poit syetry?

6 Ptters d Idutive Resoig Ne: Period: Dte: I eh of the followig ptters: i. Drw or write the ext four stges ii. Desribe the ptter. iii. Write the rule s lgebri expressio i ters of (the stge uber). Expressio B (oe will be used ore th oe!): ( + ) ( ) Questio # Desribe ptter Write the rule (expressio) Strt t, dd 3 for eh stge ) Coplete the ext 2 stges of the figures below. b) Me tble for the uber of shded squres i eh figure d write the rule ) Me tble for the uber of shded squres i eh figure d write the rule 2. The figure below shows the first 3 stges of frtl. How y irles will the th stge of this frtl oti? (Hit: drw the ext stge, e tble, desribe the ptter, d the write the rule s lgebri expressio.)

7 3. The squres below re rrged i sequee to show ptter. The tble below shows the perieter of eh figure fored by the squres i the five ptter stges. Eh side of squre represets uit. If this ptter were to otiue, Write the perieter of the 6 th, 7 th, 8 th d 9 th figure d forul or expressio You ould use to deterie the perieter of the figure t stge. 4. Study the tble d oplete the ext 2 stges C you fid rule for the tble? 5. The blos below re rrged i sequee to show ptter. Coplete the ext 2 stges d write the rule. 6. Coplete the ext 4 stges of this ptter d desribe the ptter: 0,,, 2, 3, 5, 8, 3,... (Hit: It's the Fiboi sequee!) You do ot eed to write the rule. 7. Coplete the ext 3 stges d desribe how the ext stge is fored.

8 Fidig Agles i Trigles Ne Dte Pd Usig wht you ow bout gles i trigles, prllel lies, d other gle reltioships, fid the issig gles i eh of the followig probles. *Hit loo t ALL of the s i the digr.*. = b = 2. = = = d = = p = e = f = r = s = 33 t = v = 60 p 0 v t r s 3. = b = = d = e = f = g = h = j = = = e d j b g f h

9 4. = b = = d = l 3 l 4 e = f = l l 2 d l 3 l 4 g = h = = = = p = s = 72 g b d h e f l p s 50 l 2 5. = b = = d = e = f = g = h = j = = = = p = q = r = s = v = s r p q j d 76 e g h 0 b v 82 f

10 Fidig Agles i Polygos Ne Dte Pd Usig wht you ow bout gles i trigles d polygos, prllel lies, d other gle reltioships, fid the issig gles i eh of the followig probles or swer the questio relted to the piture show.. b = 2. = 43 b Wht is wrog with this piture? = = r 36 p = q = r = s = t = 6 u 06 p q 60 v u = v = w = x = y = z = s t z 22 x w 77 y 87

11 5. = b = j b = d = e = g = g h h = = j d e 6. = b = = g d = e = e h f = g = j h = j = = = f d b = 7. = b = = = = = d = b = d 94 56