Maths: Symmetry 😴

• The two parts on either side of an axis of symmetry are equal in shape and area.
• If two parts of a figure are equal in shape and area but do not coincide after folding, the line is not an axis of symmetry
• A plane figure has rotational symmetry if it coincides with its original position after less than a complete rotation.
• The point about which a figure is rotated for rotational symmetry is called the centre of rotation
• Steps to find rotational symmetry of a rectangle using a plastic paper

  1️⃣ Draw a rectangle ABCD and mark its centre as O

  2️⃣ Copy the rectangle onto a plastic paper

  3️⃣ Overlap the plastic paper with the original figure

  4️⃣ Rotate the plastic paper about point O

  5️⃣ Observe the number of times the figures coincide
• The number of times a figure coincides with itself during one complete rotation is called its order of rotational symmetry
• The centre of rotation of a square is the intersection of its axes of symmetry.
• A parallelogram has rotational symmetry but no axes of bilateral symmetry.
• If a bilaterally symmetrical figure also has rotational symmetry, its order of rotational symmetry equals the number of axes of symmetry.
• The centre of rotational symmetry of a bilaterally symmetrical figure is the intersection of its axes of symmetry
• What is rotational symmetry?

  Coincides with original position
• The order of rotational symmetry of a figure that has rotational symmetry is greater than 1
• The order of rotational symmetry is the number of times a figure coincides with its original position during a complete rotation.
• Match the type of triangle with its description according to the lengths of its sides:

  Equilateral triangle ↔️ All three sides are equal

  Isosceles triangle ↔️ Two sides are equal

  Scalene triangle ↔️ All three sides are unequal
• The sum of the three interior angles of a triangle is 180 degrees.
• Steps to find the sum of the interior angles of a triangle

  1️⃣ Draw any triangle on paper

  2️⃣ Cut out the three angles

  3️⃣ Paste the angles on a straight line without overlapping

  4️⃣ Measure the sum of the pasted angles
• The sum of the interior angles of a triangle is 180 degrees.
• The sum of the four interior angles of a quadrilateral is 360 degrees.
• The sum of the interior angles of a quadrilateral is 360 degrees.
• Match the part of the quadrilateral with its property:

  Triangle ABC ↔️ Sum of angles is 180°

  Quadrilateral ABCD ↔️ Sum of angles is 360°
• An exterior angle of a triangle is formed by producing one of its sides.
• What is the sum of the exterior angles of a triangle?

  360 degrees
• The three exterior angles of a triangle can be positioned as angles around a point.
• The sum of the exterior angles of a triangle is 360
• What is the sum of the exterior angles of a quadrilateral?

  360 degrees
• A quadrilateral has four exterior angles, one at each vertex.
• The sum of the exterior angles of a quadrilateral is 360
• What is the sum of an interior and an exterior angle at one vertex of a triangle?

  180 degrees
• At each vertex of a quadrilateral, the sum of the interior and exterior angle is 180 degrees.
• If the exterior angles of a quadrilateral are 110°, 140°, 85°, what is the fourth exterior angle in degrees?25
• According to the figure, what is ACD equal to?

  a + b