3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles.

Transcription

1 3 ngle Geometry MEP Prtie ook S3 3.1 Mesuring ngles 1. Using protrtor, mesure the mrked ngles. () () (d) (e) (f) 2. Drw ngles with the following sizes. () 22 () (d) 90 (e) 153 (f) 45 (g) 180 (h) Mesure these ngles. () () 2 3

2 MEP Prtie ook S3 4. Drw ngles with the following sizes. () 195 () For eh tringle, mesure eh ngle nd dd up the three ngles otined. () () Wht do you onlude? 6. For eh qudrilterl, mesure ll the interior ngles nd find the sum. () () 3.2 Line nd Rottionl Symmetry 1. Copy eh shpe elow, mrk ll lines of symmetry nd stte the order of rottionl symmetry. () () (d) (e) (f) 2 4

3 MEP Prtie ook S3 (g) (h) (i) 2. Copy nd omplete eh shpe elow so tht they hve line symmetry ut no rottionl symmetry. Mrk your lines of symmetry. () () 3. Copy nd omplete eh shpe elow so tht they hve rottionl symmetry ut no line symmetry. In eh se stte the order of rottionl symmetry. () () (d) 4. Copy nd omplete eh of the following shpes, so tht they hve oth rottionl nd line symmetry. In eh se drw the lines of symmetry nd stte the order of the rottionl symmetry. () () (d) 5. Drw shpe with etly 5 lines of symmetry. 2 5

4 MEP Prtie ook S3 3.3 ngle Geometry 1. Clulte the size of the ngles mrked with letter in eh digrm. None to sle () () (d) (e) (f) d e f 30 g (g) (h) j (i) k 33 h 22 i 35 l (j) (k) (l) n p m (m) (n) s (o) q r v 33 u t Find the ngles mrked with letter in eh retngle elow. () ()

5 MEP Prtie ook S3 3. The frmework of symmetril roof is illustrted elow. is perpendiulr to C. 40 Find the size of the ngles mrked, nd. C 4. Write down n eqution tht is stisfied in eh of the following digrms. In eh se, solve the eqution for. 2 () () (d) (e) (f) ngles with Prllel nd Interseting Lines 1. Clulte the unknown ngles in the following digrms. () () e d

6 MEP Prtie ook S3 (d) (e) (f) f g h º (g) (h) (i) 63 f p e d (j) (k) (l) 67 e 25 m 85 e 80 g f 57 (m) (n) (o) s (p) (q) (r) p 69 e (s) (t) y

7 MEP Prtie ook S3 2. For eh digrm, find n eqution in, nd hene solve for. () () Find the vlues of the unknown ngles in eh of the following. () 126 () (d) (e) (f) 4e 3e 5e f 72 g CD is rhomus. D 27 C ngle DC = 27 The digonls C nd D ross t. Clulte the size of the ngle DC. 2 9

8 MEP Prtie ook S3 5. The pentgon CDE is the frme for Irhim's mountin ike. E C is n isoseles tringle in whih Not to sle = C nd ngle C = 65. D In the qudrilterl CDE ngle CD = 70, ngle CE = 90 nd C is prllel to ED. () (i) Clulte the size of ngle C. (ii) Wht fts out the ngles of tringle did you use in your lultion? () Clulte the size of the ngle CDE. 3.5 ngle Symmetry in Polygons C (MEG) 1. Find the sum of the interior ngles of () qudrilterl () pentgon. 2. Find the size of eh interior ngle of () regulr hegon () regulr nongon. 3. Find the numer of sides of polygon if the sum of its interior ngles is () 1800 () Eh interior ngle of regulr polygon is 140. Find the numer of sides of the polygon. 5. Eh interior ngle of regulr n-gon is 168. Wht is the vlue of n? 6. Find the vlue of in eh of the following digrms. () () (d) (e) (f)

9 MEP Prtie ook S3 7. The ngles of qudrilteril re 3, 4, 5 nd 6. () Find. () Wht re the ngles in degrees? 8. () () For eh digrm ove, show three different wys of shding prts of the shpes so tht they hve line symmetry ut no rottionl symmetry. Shde setions of one shpe so tht it hs rottionl symmetry of order 2 ut no lines of symmetry. Is it possile to do this for oth shpes? Repet () for rottionl symmetry of order 3. (d) Repet () for rottionl symmetry of order () regulr polygon hs n interior ngle of 175. How mny sides does it hve? () seond regulr polygon hs n interior ngle whih is 1 smller. How mny sides does it hve? Is it possile for regulr polygon to hve n interior ngle of 173? 10. () The digrm shows prt of tiling pttern of regulr pentgons nd nother shpe. 108 (i) Whih of the following orretly desries the shded shpe: squre, rhomus, trpezium, retngle, prllelogrm, kite? (ii) Clulte the size of the ngle mrked. (iii) regulr pentgon hs rottionl symmetry. Wht is the order of rottionl symmetry of regulr pentgon? 3 1

10 MEP Prtie ook S3 () nother tiling pttern is formed using regulr otgons nd squres, s shown. y Clulte the size of the ngle mrked y. Drw tiling pttern using regulr hegons only. You must drw t lest five hegons. (SEG) 3.6 Symmetry Properties of 3D Shpes 1. The following solids hve rottionl symmetry. For eh of them, stte the order of rottionl symmetry out the given is. () () 2. For eh of the following prisms, opy eh digrm nd drw n is so tht the order of rottionl symmetry out tht is is 2. () () 3 2

11 MEP Prtie ook S3 3. In the given prism, the ross-setion is in the shpe of regulr pentgon. Drw () () n is ST so tht the order of rottionl symmetry out ST is 2; n is XY so tht the order of rottionl symmetry out XY is Stte the order of rottionl symmetry out eh of the es shown. ll the 12 edges of the solid re equl in length. () () 5. P R S For the solid ove, find the order of its rottionl symmetry out () PQ () RS. Q 6. () ue hs 9 plnes of symmetry. Drw digrms to show these plnes. () ue hs 3 es of rottionl symmetry of order 4. Drw digrms to show these es. The digrm of ue opposite shows one is of rottionl symmetry of order 3. There re 3 other es with the sme order. Drw digrms to show these es. (d) There re 6 es with symmetry of order 2. Drw digrms to show these es. 7. Drw solid tht hs one is of symmetry nd rottionl symmetry of order 5 out the is. 3 3

12 MEP Prtie ook S3 3.7 Compss erings 1. The mp elow shows the positions of some villges. rgfoot Hrome N W E S Sheepwsh Cove West Leigh rtton Sle: 2 miles to 1 m () () (d) (e) Whih villge is due north of Sheepwsh? Whih villge is due west of Cove? Wht is the ompss diretion of Sheepwsh from West Leigh? How mny miles is (i) rtton from Cove (ii) Hrome from rgfoot? Mke tring of the mp nd mrk the positions of (i) Drley, whih is 3 miles due south of Hrome, (ii) Lee, whih is 4 miles south est of rgfoot. 2. For eh of the following, write down the ering of from. () () (d)

13 MEP Prtie ook S P 106 Q Wht is the ering of () Q from P () P from Q? Wht is the ering of () T from S? () S from T? S 60 T 5. Drw digrm with 4 towns mrked, so tht tht three of the towns re equidistnt from the fourth town, P, nd hve erings from P of () 036 () field is in the shpe of squre, with orners W, X, Y nd Z. Z 135 The ering of Y from Z is 135. W Y Find the ering of () Y from X () W from Z. X 7. Wht is the ering of () from () from from (d) from? 8. The figure shows the positions of P, Q nd R. Wht is the ering of () Q from P () P from Q R from P (d) P from R (e) Q from R (f) R from Q? P Q 100 R 9. point is 280 m due of the point. mn wlks from in the diretion 050. Clulte how fr he wlks efore he is () equidistnt from nd, () s lose s possile to, due est of. 3 5

14 MEP Prtie ook S3 3.8 ngles nd Cirles 1 1. Find the ngles mrked with letter in eh of the following digrms. (In eh se is the entre of the irle.) () 55 () (d) e d d e (e) (f) Find the ngles mrked with letter in eh digrm elow. (In eh se is the entre of the irle.) () 30 is tngent 3 6

15 MEP Prtie ook S3 () 70 C nd C re tngents 3. Find the ngles mrked with letters in eh of the following digrms. (In eh se is the entre of the irle.) () () (d) Find the dimeter of eh irle elow. (In eh se is the entre of the irle. () 8 6 ()