SYMMETRIES: A symmetry is a rigid transformation of a figure onto itself. For example, an equilateral triangle ABC may be: @ rot at ed 120 (so t hat A6B, B6C and C6A) [[ (A,B,C) ]] Ao @ rotated 240 (A6C, B6A and C6B). [[ (A ,C,B) ]]o (Examples of point symmetry or rotational symmetry) B CThe t riangle may also be: @ reflected through the altitude from A ... A stays put, B6C, C6B ... (A) (BC) @ reflected through the altitude from B [[ (B) (A,C) ]] @ reflected through the altitude from C. [[ (C) (A ,B) ]] (Examples of line symmetry)A C BA C B C A B CA C B BA12123I F F D D D Rotate 360 Rotate 120 Rotate 240 Flip over Flip over Flip overoo o (identity) altitude A altitude B altitude C (A)(B)(C) (ABC) (ACB) (A) (BC) (B)(AC) ( )( )Together with the 360 rotational symmetry (w hich is tantamount to leaving the figure alone!), whichoevery f igure has, these symmetries form " the symmet ry group of an equilateral t riangle" .1. The letter A has line symmetry. Draw the line of reflection, or line of symmetry.2. The letter B also has line symmetry. Check out these: C D E F Z 3. Do any of these letters have rotational symmetry?A B C D E F G H I J K L MN O P Q R S T U V W X Y Z4. Find all the symmetries of each of the follow ing:a. isosceles triangle regionb. scalene quadrilateralc. isosceles trapezoid regiond. parallelogram regione. rhombus regionf. squareg. regular hexagon regionh. circular regioni. the figure at right ü5. Name a figure that has TRANSLATIONAL SYMMETRY!6. Add one square to this figure so that it will have one line & no rotational symmetry.Add one square to this figure so that it will have one rotational & no line symmetry.SYMMETRIES: A symmetry is a rigid transformation of a figure onto itself. For example, an equilateral triangle ABC may be: @ rot at ed 120 (so t hat A6B, B6C and C6A) [[ (A,B,C) ]] Ao @ rotated 240 (A6C, B6A and C6B). [[ (A,C,B) ]]o (Examples of point symmetry or rotational symmetry) B CThe t riangle may also be: @ reflected through the altitude from A ... A stays put, B6C, C6B ... (A) (BC) @ reflected through the altitude from B [[ (B) (A,C) ]] @ reflected through the altitude from C. [[ (C) (A ,B) ]] (Examples of line symmetry)A C B A C B B C A B CA C B B A A C12123I F F D D D Rotate 360 Rotate 120 Rotate 240 Flip over Flip over Flip overoo o (identity) altitude A altitude B altitude C (A)(B)(C) (ABC) (ACB) (A) (BC) (B)(AC) ( AB )( C )Together with the 360 rotational symmetry (w hich is tantamount to leaving the figure alone!), whichoevery f igure has, these symmetries form " the symmet ry group of an equilateral t riangle" .1. The letter A has line symmetry. Draw the line of reflection, or line of symmetry. None None2. The letter B also has line symmetry. Check out these: C D E F Z See below3. Do any of these letters have rotational symmetry?180E 180EA B C D E F G H I J K L M 180E *180E 180E 180E 180EN O P Q R S T U V W X Y Z *A circle has infinitely many rotational symmetries; the lett er O here is not a perfect circle.4. Find all the symmetries of each of the follow ing:a. isosceles triangle regionb. scalene quadrilateralc. isosceles trapezoid region 90E,d. parallelogram region 180E, 360E 180E, 270E,e. rhombus region 180E, 360E 360Ef. square 60E 360E g. regular hexagon region 120E 300Eh. circular region The circlehas infinitely many i. the figure at right ü 180E, 360E line & rotat ional 180E 240ESymmetri es 5. A line can be translated along its length. A plane. A frieze design. 6A6A. Add one square to this figure ...so that it w ill have one line & no rotational symmetry.6B. ...so that it w ill have one rotational & no line symmetry. 6BOther creative solutions to #5& 6 exist, but w e show the most obvious