Grade 7 / Axial and central symmetry 71 exercises (100% corrected)

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ABC(d ABC(d 4231 (d (d ChingQuizz : 1 exercise available for Quizz assessment : 1. Axial symmetry: reminders E.5615 Consider in the frame below the triangle ABC and the line ( d ) . 1 Place the following in the box above : a The point A symmetrical to the point A relative to the line ( d ) . b The point B symmetric of the point B relative to the line ( d ) . c The point C such that C and C are symmetric about the line ( d ) . 2 Draw the triangle A B C . E.10772 In the frame below, consider the triangle ABC and the straight line ( d ) . Draw the image of triangle ABC by symmetry of axis ( d ) . E.10869 Consider the 5 ducks below : Which duck is the image of the axially symmetrically hatched duck? E.10876 A gray polygon is shown below : Construct the symmetric of this polygon relative to the line ( d ) . E.10874 Symmetrize the two polygons below relative to each of their axes. https://chingmath.fr chapExoCorrec/5615 sacados/5615 ABC(d chapExoCorrec/10772 sacados/10772 ABC(d chapExoCorrec/10869 sacados/10869 4231 chapExoCorrec/10876 sacados/10876 (d chapExoCorrec/10874 sacados/10874 (d
ABC(d) (d ABCEFG E.10909 Consider the line segment ( d ) and the figure below composed of the triangle ABC , the semicircle C with diameter [ AB ] and : Draw the image of the figure by the axis of symmetry ( d ) . E.5616 Complete the figure below so that it admits the line ( d ) for axis of symmetry: E.10875 Symmetrize the two polygons below relative to each of their axes. E.10878 Reminder : The median of a segment [ AB ] is the unique line ( d ) that satisfies the following two properties : The line ( d ) passes through the midpoint of the segment [ AB ] . The line ( d ) is perpendicular to the line ( AB ) . Consider the figure below representing two triangles : 1 Draw the perpendicular bisector ( d ) of the segment [ AE ] using a ruler and a set square. 2 Check that the line ( d ) is also the perpendicular bisector of the segment [ BF ] . 3 What else needs to be checked to confirm that triangle EFG is the image of triangle ABC under the symmetry axis ( d ) ? 2. Axial symmetry: symmetry of a line E.5617 Shown below are three straight lines ( d ) , ( d ) and (Δ) . https://chingmath.fr chapExoCorrec/10909 sacados/10909 ABC(d) chapExoCorrec/5616 sacados/5616 (d chapExoCorrec/10875 sacados/10875 chapExoCorrec/10878 sacados/10878 ABCEFG chapExoCorrec/5617 sacados/5617
xBy (d(d (d(d 011xyAB 011xyAB (Your construction features should not extend beyond the pro-posed frame.) 1 Draw the symmetric of the angle ∠ xBy by axial symme-try of axis (Δ) . 2 Give the measures of the angle ∠ xBy and its symmetri-cal. E.5618 Shown below are three straight lines ( d ) , ( d ) and (Δ) . Using plots of your choice, justify that the straight line ( d ) admits as image the straight line ( d ) through axial symmetry of axis (Δ) . E.6559 Shown below are three straight lines ( d ) , ( d ) and (Δ) : Is the line ( d ) the symmetrical of the line ( d ) with respect to the line (Δ) ? Justify your answer. 3. Axial symmetry and benchmark E.10862 In the plane with a reference point : 1 Give the coordinates of points A and B . 2 a Place the points A and B images of the points A and B by y-axis symmetry. We will also draw the seg-ment [ A B ] . b Give the coordinates of the points A and B . E.10867 In the plane with a reference point : 1 Give the coordinates of points A and B . 2 a Place the points A and B symmetrical about the x-axis of the points A and b respectively. The segment [ A B ] will also be drawn. b Give the coordinates of the points A and B . https://chingmath.fr xBy chapExoCorrec/5618 sacados/5618 (d(d chapExoCorrec/6559 sacados/6559 (d(d chapExoCorrec/10862 sacados/10862 011xyAB chapExoCorrec/10867 sacados/10867 011xyAB
011xyAB(d 011xyAB(d 011xyAB(d 4312 1234 E.10868 In the plane with a reference point : 1 Give the coordinates of points A and B . 2 a Place the points A and B images of the ends of the segment [ AB ] by symmetry of axis ( d ) . b Give the coordinates of the points A and B . E.10908 In the reference frame below, con-sider the line ( d ) and the segment [ AB ] . 1 Draw segment [ A B ] image of segment [ AB ] by straight line ( d ) . 2 Give the coordinates of the points A and B ’ E.11012 In the coordinate system below, consider the line ( d ) and the segment [ AB ] . 1 Draw the segment [ A B ] , which is the image of the seg-ment [ AB ] under the line ( d ) . 2 Give the coordinates of points A and B 4. Central symmetry: introduction E.11535 Consider the five ducks below : Is the hatched duck the image of one of the other ducks ro-tated by 180 degrees? Which one? Can you indicate the center of this rotation? E.11615 Consider five right triangles : Is the shaded triangle the image of another triangle after a half-turn? Which one? Can you indicate the center of this half-turn? https://chingmath.fr chapExoCorrec/10868 sacados/10868 011xyAB(d chapExoCorrec/10908 sacados/10908 011xyAB(d chapExoCorrec/11012 sacados/11012 011xyAB(d chapExoCorrec/11535 sacados/11535 4312 chapExoCorrec/11615 sacados/11615 1234
OAC1 OBCAAC2 OA1 OABC2 E.171 Definition: Point A is said to be the image of point A under the symmetry with center O , if point A is obtained by rotating point A through half a turn ( 180 o ) . 1 In the context 1 : Below are the points A , O , and the circle C with center O passing through the point A . Let A be the image of point A under the symmetry with center O . What does the segment [ AA ] represent for the circle C ? Place the point A . 2 In the frame 2 : Below are the five points A , A , B , C , O and the circle C with center O passing through point B . a What must be drawn to prove that point A is the image of point A under the symmetry with center O ? b Place point B , the image of point B under the sym-metry with center O , on circle C . c Draw triangles ABC and its image A B C by symme-try with center O . E.1921 1 In frame 1: Below, we consider the two points A and O as well as the half-line [ AO ) : We denote A as the image of point A under the symme-try with center O . a Several points have been placed on the ray [ AO ) . Us-ing a compass, place point A on the plane. b What does point O represent for segment [ AA ] ? 2 In box 2: In the frame below, consider the four points A , B , C , O and the two half-lines [ AO ) and [ BO ) : a Using a compass, place points A and B , which are the respective images of points A and B under the symmetry center O . b Place point C , the image of point C , using the sym-metry center O . c Draw triangle ABC and its image A B C using the symmetry center O . Proposition: Let A and O be two points on the plane. The image A of point A by the symmetry with center O is the only point in the plane such that point O is the mid-point of segment [ AA ] . Method : To draw point A , mirror image of point A about center O . 1 Draw line segment [ AO ) . 2 Using a compass, place point A such that AO = OA . Note: O becomes the midpoint of segment [ AA ] . 5. Central symmetry: symmetry of lines and half-lines https://chingmath.fr chapExoCorrec/171 sacados/171 OAC1 OBCAAC2 chapExoCorrec/1921 sacados/1921 OA1 OABC2
O(dAB OAB O(d IJ E.10179 Shown below are the straight line ( d ) , the points A and B belonging to ( d ) and the point O : 1 Draw the symmetries of points A and B by central sym-metry of center O . 2 Draw the line ( d ) symmetrical to the line ( d ) with re-spect to the point O . E.1254 Consider the figure below composed of a half-line [ AB ) and a point O of the plane : 1 a Place the point A image of the point A by central symmetry of center O . b Place the point B image of the point B by the central symmetry of center O . 2 Draw the symmetric of the half-line [ AB ) by central sym-metry of center O . E.10175 Below are the two lines ( d ) and (Δ) and the point O : Draw lines ( d ) and (Δ ) , which are respectively images of lines ( d ) and (Δ) through the center of symmetry O . Hint: You can use the intersection point of lines ( d ) and (Δ) . 6. Central symmetry and grid E.1269 Draw the symmetries of the two fig-ures relative to each of their centers of symmetry. Use the grid to help you. E.1261 Draw the symmetries of the figures with respect to the point associated with each of the figures : https://chingmath.fr chapExoCorrec/10179 sacados/10179 O(dAB chapExoCorrec/1254 sacados/1254 OAB chapExoCorrec/10175 sacados/10175 O(d chapExoCorrec/1269 sacados/1269 IJ chapExoCorrec/1261 sacados/1261
IJKL AGMSBHNTCIOUDJPVEKQWFLRX 011xyAB E.1267 Using the grid, draw the image of these three figures using the central symmetries whose centers are located next to each of these figures : E.6561 The figure below is composed of 15 squares juxtaposed against each other : We perform the following move program : We start from the point E . We move by symmetry of center I . Then, following the axis symmetry ( UI ) . Then, following the symmetry of center J . Then, following the axis symmetry ( AV ) . Without justification, give the arrival point after performing this travel program. 7. Benchmark and central symmetry E.10677 In the plane with a reference point : 1 Give the coordinates of points A and B . 2 a Draw the segment [ A B ] image of the segment [ AB ] by center symmetry O (0 ; 0) . b Give the coordinates of the points A and B . https://chingmath.fr IJKL chapExoCorrec/1267 sacados/1267 chapExoCorrec/6561 sacados/6561 AGMSBHNTCIOUDJPVEKQWFLRX chapExoCorrec/10677 sacados/10677 011xyAB
011xyAB 011xyAB 011xyAB xxyy-5-4-3-2-1012345-5-4-3-2-112345 011xyABK E.10678 In the plane with a reference point : 1 Give the coordinates of points A and B . 2 a Draw the segment [ A B ] image of the segment [ AB ] with respect to symmetry of center O (0 ; 0) . b Give the coordinates of the points A and B . E.10679 In the plane provided with a refer-ence frame, consider the segment [ AB ] shown below : 1 Give the coordinates of points A and B . 2 a Draw the image of the segment [ AB ] by symmetry of center O (0 ; 0) . b Give the coordinates of the points A and B . E.10680 In the plane provided with a refer-ence frame, consider the segment [ AB ] shown below : 1 Give the coordinates of points A and B . 2 a Draw the segment [ A B ] image of the segment [ AB ] by center symmetry O (0 ; 0) . b Give the coordinates of the points A and B . E.1974 1 Place the following points in the frame below : A (2 ; 1) ; B (4 ; 3) ; C ( − 1 ; 4) Draw the triangle ABC in blue. 2 a Draw the symmetrical A of the point A relative to the line ( xx ) . What are the coordinates of the point A ?. b Draw, in red, the symmetric of the triangle ABC with respect to ( xx ) . 3 a Draw the symmetrical A  of the point A with re-spect to the origin of the reference frame. What are the coordinates of the point A  ?. b Draw, in green, the symmetric of the triangle ABC with respect to the origin of the reference frame. E.10907 In the reference frame below, con-sider the segment [ AB ] and the point O . 1 Give the coordinates of the three points A , B , K . 2 a Draw [ A B ] the image of the segment [ AB ] by sym-metry of center K . b Give the coordinates of the points A and B . https://chingmath.fr chapExoCorrec/10678 sacados/10678 011xyAB chapExoCorrec/10679 sacados/10679 011xyAB chapExoCorrec/10680 sacados/10680 011xyAB chapExoCorrec/1974 sacados/1974 xxyy-5-4-3-2-1012345-5-4-3-2-112345 chapExoCorrec/10907 sacados/10907 011xyABK
011xyABK ABCO ABCO ABCDO OABC E.11013 In the reference frame below, con-sider the segment [ AB ] and the point O . 1 Give the coordinates of the three points A , B , K . 2 a Draw [ A B ] the image of the segment [ AB ] by sym-metry of center K . b Give the coordinates of the points A and B . 8. Central symmetry and white paper E.10905 Consider the triangle ABC below : Construct triangle A B C image of triangle ABC by central symmetry of center O . E.10176 Shown below are the triangle ABC and the point O . Draw triangle A B C symmetrical to triangle ABC through point O . E.1256 Draw the symmetric of the rectangle ABCD with respect to the center O : E.10177 1 Draw the triangle ABC such that : AB = 6 cm ; ∠ CAB = 40 o ; AC = 4 cm 2 Place a point O outside the triangle ABC ; draw the symmetric of the triangle ABC with respect to O . E.10180 Draw the symmetries with respect to O of the figures below : https://chingmath.fr chapExoCorrec/11013 sacados/11013 011xyABK chapExoCorrec/10905 sacados/10905 ABCO chapExoCorrec/10176 sacados/10176 ABCO chapExoCorrec/1256 sacados/1256 ABCDO chapExoCorrec/10177 sacados/10177 chapExoCorrec/10180 sacados/10180 OABC
S 5cm4cmABCDE(d O O E.1259 Draw the symmetric of the figure below with respect to the point S . E.1257 The figure below is composed of a square, an isosceles triangle, a semicircle whose diameter is one of the sides of the square and a straight line ( d ) extending a diagonal of the square : Reproduce this figure, then draw the symmetrical of this fig-ure with respect to the point E . E.1258 Draw the symmetric of the figure below with respect to the point O . (leave traces of your con-structions) E.1260 On the figure below all rounded parts are semicircles, draw the symmetrical of this figure with respect to the point O : E.1971 1 Draw the triangle ABC such that : AB = 6 cm ; CAB = 40 o ; AC = 4 cm 2 Using compass and ruler, draw the center I of the cir-cumscribed circle of the triangle ABC . 3 Place a point O outside the triangle ABC ; draw the symmetric of the triangle ABC with respect to O . 4 Draw the circumscribed circle of triangle A B C . https://chingmath.fr chapExoCorrec/1259 sacados/1259 S chapExoCorrec/1257 sacados/1257 5cm4cmABCDE(d chapExoCorrec/1258 sacados/1258 O chapExoCorrec/1260 sacados/1260 O chapExoCorrec/1971 sacados/1971
ABCD(d ABC(d ABCDEFGH E.11627 Draw the symmetric of the rectangle ABCD relative to the line ( d ) . E.11628 In the frame below, consider the trian-gle ABC and the straight line ( d ) . 1 Place the following points in the frame above : a The point A symmetrical to the point A relative to the line ( d ) . b The point B symmetrical to the point B relative to the line ( d ) . c The point C such that C and C are symmetrical rel-ative to the line ( d ) . 2 Draw the triangle A B C . E.11629 Consider the figure shown below com-posed of two quadrilaterals. Show that this figure does not have an axis of symmetry. Jus-tify your approach. 9. Central symmetry: properties E.1266 1 Draw the triangle ABC such that : AB = AC =7 cm ; BAC =115 o 2 Construct the point A symmetrical to the point A with respect to the line ( BC ) . 3 Construct the point B symmetrical of the point B with respect to the point A . 4 Construct the point C symmetrical of the point C with respect to the point A . 5 What can be said about the relative position of the straight lines ( BC ) and ( B C ) ? Justify. 6 What is the nature of the triangle AB C ? Justify your answer. 7 Draw the height of the triangle ABC from B https://chingmath.fr chapExoCorrec/11627 sacados/11627 ABCD(d chapExoCorrec/11628 sacados/11628 ABC(d chapExoCorrec/11629 sacados/11629 ABCDEFGH chapExoCorrec/1266 sacados/1266
ABCDEFGHO 4132 ABCEDF E.1265 1 Draw the triangle ABC such that : AB = 4 cm ; BC = 5 cm ; AC = 6 cm 2 Place a point O such that the segment [ AO ] measures three-quarters of [ AC ] . 3 Draw the symmetrical A B C of the triangle ABC with respect to the point O . 4 What can we say about the segments [ AB ] and [ A B ] ? Subsidiary question: 5 Justify that the point C is the midpoint of the segment [ AC ] . E.6560 Consider the two quadrilaterals ABCD and EFGH symmetrical about the point O : Copy and complete the following sentences : 1 The points A and . . . are two symmetric points. 2 The segment [ DC ] admits the segment . . . as symmetric. 3 The segments [ AB ] and . . . have the same . . . . 4 angles ∠ GFE and ∠ ABC have the same . . . . 5 polygons ABCD and EFGH have the same . . . . 6 The straight lines ( BD ) and . . . are . . . . 10. Central symmetry: search for the center of symmetry E.10870 Consider the five ducks below : Which duck is the image of the hatched duck with respect to a central symmetry? E.1268 The triangle DEF was obtained from the triangle ABC by central symmetry: the aim of this question is to find the center of symmetry: 1 Knowing that the triangle DEF was obtained by the central symmetry of the triangle ABC , complete the fol-lowing sentences : The image of the point A is the point . . . . . . The image of the point B is the point . . . . . . The image of the point C is the point . . . . . . 2 Draw the segments [ AE ] , [ BD ] and [ CF ] . What do you notice? 3 Name O the point of conjunction of these segments. What property must be checked to show that the points A and E are symmetrical with respect to the point O ? 4 Verify also that the following pairs of points admit the https://chingmath.fr chapExoCorrec/1265 sacados/1265 chapExoCorrec/6560 sacados/6560 ABCDEFGHO chapExoCorrec/10870 sacados/10870 4132 chapExoCorrec/1268 sacados/1268 ABCEDF
GHIJNKML ABCDEFG point O as center of symmetry: B ; D et C ; E E.10178 Consider the figure below : In this question we will show that the quadrilateral KNLM cannot be obtained by the symmetric of the quadrilateral IJGH : 1 If the quadrilateral IJGH were the symmetric of the quadrilateral KNLM , complete the sentences : The image of point I is the point . . . . . . The image of point J is point . . . . . . The image of point G is point . . . . . . The image of point H is point . . . . . . 2 Draw each of the segments connecting a point on the IJGH quadrilateral to the assumed symmetric point. 3 What do you notice? Conclude. E.10906 Consider the two quadrilaterals be-low : Justify that these two quadrilaterals are not images of each other by central symmetry. Hint: you must use the points by naming them, leave your construction plots and justify your constructions and rea-soning with sentences. E.1262 In each case, determine whether the given point is a center of symmetry or find if it is : E.10181 In each case, determine whether the given point is a center of symmetry or find the if it is : E.1973 Consider the polygon ABCD , the segment [ EF ] , and the point G below 1 Prove that segments [ AB ] and [ EF ] are images of each other through central symmetry. Place point O at the center of this symmetry. 2 Prove that point G is the image of point C under the symmetry with center O . 3 Draw the polygon EFGH , which is the image of the polygon ABCD under the symmetry with center O . https://chingmath.fr chapExoCorrec/10178 sacados/10178 GHIJNKML chapExoCorrec/10906 sacados/10906 chapExoCorrec/1262 sacados/1262 chapExoCorrec/10181 sacados/10181 chapExoCorrec/1973 sacados/1973 ABCDEFG
ab xy011xy011 ABCDEFGHIJKL abcdefghijkl M1M2M3M4 E.1263 Study the following two figures to determine whether or not a center of symmetry is present : E.1264 Study each of the two figures below to determine whether or not it has a center of symmetry: If the figure has a center of symmetry, give the coordi-nates of the center of symmetry. If the figure has no center of symmetry, justify your state-ment. ( Points can be named if necessary) 11. Axis and center of symmetry E.5619 Three quadrilaterals are shown be-low : ABCD is a rhombus ; EFGH is a rectangle; IJKL is a square. Draw and specify the centers and axes of symmetry of each of these quadrilaterals. E.6479 Which of the following signs have one or more axes of symmetry: For each sign, give the number of axes of symmetry that it admits. 12. Central symmetry and plane tessellation E.10871 Consider the following tiling: https://chingmath.fr chapExoCorrec/1263 sacados/1263 ab chapExoCorrec/1264 sacados/1264 xy011xy011 chapExoCorrec/5619 sacados/5619 ABCDEFGHIJKL chapExoCorrec/6479 sacados/6479 abcdefghijkl chapExoCorrec/10871 sacados/10871 M1M2M3M4
C0C1C2C3 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172 ABCDI JesaisJ’utiliseJ’endéduisSideuxcerclesontmêmerayonetsileurscentressontsymétriquesalorscescerclessontsymétriquesLes cercles de rayonADetdecentres respectifsAetCsont symétriques JesaisJ’utiliseJ’endéduisLe pointAest l’image du pointCpar la symétriede centreI;CDAB.Les cercles de rayonDCet de centres respectifsAetCsont symétriques. JesaisJ’utiliseJ’endéduisDetBsont les intersections des deux cercles decentresAetCet de rayons respectifsADetCD.L’image d’une intersection par une symétrie cen-trale est l’intersection des images.Le pointDa pour symétrique le pointB 1 Place the center of symmetry that transforms the rhom-bus M 1 into the rhombus M 2 . 2 Place the center of symmetry that transforms rhombus M 3 into rhombus M 4 . E.10873 Below is a tiling of the plane : 1 Determine the center of symmetry that transforms pat- tern C 0 into pattern C 1 . 2 Determine the center of symmetry that transforms pat-tern C 2 into pattern C 3 . E.10910 Consider the frieze below : 1 Determine the center of symmetry transforming pattern 16 with pattern 55 . 2 Determine the center of symmetry transforming pattern 21 with pattern 48 . 13. Complete the symmetry of a figure E.1972 For each of the figures below, color the minimum disk so that each has a center of symmetry. a b 14. Unclassified exercises E.2070 Consider a non-crossing quadrilateral ABCD with the following properties : AD = BC AB = CD Let I be the midpoint of the segment [ AC ] . The following deductive chain demonstrates that : If a quadrilateral has opposite sides of equal length, then the intersection of its diagonals is its center of sym-metry. https://chingmath.fr chapExoCorrec/10873 sacados/10873 C0C1C2C3 chapExoCorrec/10910 sacados/10910 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172 chapExoCorrec/1972 sacados/1972 fichierPlus/1972/ chapExoCorrec/2070 sacados/2070 ABCDI JesaisJ’utiliseJ’endéduisSideuxcerclesontmêmerayonetsileurscentressontsymétriquesalorscescerclessontsymétriquesLes cercles de rayonADetdecentres respectifsAetCsont symétriques JesaisJ’utiliseJ’endéduisLe pointAest l’image du pointCpar la symétriede centreI;CDAB.Les cercles de rayonDCet de centres respectifsAetCsont symétriques. JesaisJ’utiliseJ’endéduisDetBsont les intersections des deux cercles decentresAetCet de rayons respectifsADetCD.L’image d’une intersection par une symétrie cen-trale est l’intersection des images.Le pointDa pour symétrique le pointB
ABCDI(AD==(BC(AB==(DC JesaisL’image deApar la symétrie de centreIestC.(AD==(BCJ’uti-liseL’imaged’unedroite,parunesymétriecentrale,estune droite parallèleJ’endé-duisL’image de la droite(ADest:::::: JesaisJ’uti-liseJ’endé-duisL’image de la droite(CDest la droite(AB JesaisDestl’intersectiondesdroites(ADet(DC.Lesdroites(ADet(CDont pour images respectives lesdroites(CBet(ABJ’uti-liseL’image d’un point d’intersection est l’intersection desimages.J’endé-duisL’image du pointDest le point:::::: AO abcd ABCDEFGH(HG==(EFIJKL(IJ==(LK(IL==(JKMNOPQRST E.2071 Consider an uncrossed quadrilateral ABCD with the following properties : ( AD ) == ( BC ) ( AB ) == ( CD ) Let I be the midpoint of segment [ AC ] . Using the deductive chain below, we’ll show that the symmet-rical point of D is none other than B ; thus, ABCD admits a center of symmetry: ABCD is a parallelogram. E.3956 Using only the compass and a straight-edge, draw the square ABCD whose center O and vertex A are shown below : E.11815 Four special quadrilaterals are shown below : For each of them : Give the nature of the quadrilateral; Draw, freehand, the axes of symmetry in the figure ; Give the number of axes of symmetry in the figure. E.6660 Below are shown five particular quadri-laterals: 1 Give the nature of each of these quadrilaterals. 2 Draw, if possible, the axes of symmetry of each of these quadrilaterals by hand. https://chingmath.fr chapExoCorrec/2071 sacados/2071 ABCDI(AD==(BC(AB==(DC JesaisL’image deApar la symétrie de centreIestC.(AD==(BCJ’uti-liseL’imaged’unedroite,parunesymétriecentrale,estune droite parallèleJ’endé-duisL’image de la droite(ADest:::::: JesaisJ’uti-liseJ’endé-duisL’image de la droite(CDest la droite(AB JesaisDestl’intersectiondesdroites(ADet(DC.Lesdroites(ADet(CDont pour images respectives lesdroites(CBet(ABJ’uti-liseL’image d’un point d’intersection est l’intersection desimages.J’endé-duisL’image du pointDest le point:::::: chapExoCorrec/3956 sacados/3956 AO chapExoCorrec/11815 sacados/11815 abcd chapExoCorrec/6660 sacados/6660 ABCDEFGH(HG==(EFIJKL(IJ==(LK(IL==(JKMNOPQRST