Congruence, symmetry and polygons

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Presentation transcript:

Congruence, symmetry and polygons Congruence and similarity Symmetry Properties of quadrilaterals Names of polygons Angles in polygons Properties of regular polygons

Congruence and Similarity Congruent is the maths word that means exactly the same All 4 of these arrows are congruent. They are the same size and shape (it doesn’t matter what direction they point in!)

Congruence and Similarity Similar means the shapes are in the same proportion, but could be a different size 3 of these arrows are similar, but are different sizes. One is not the same shape... Can you tell which one?

Symmetry A shape has a line of symmetry if the shape looks identical on each side of the line... This cross has 4 lines of symmetry.

Symmetry A shape has rotational symmetry if it can be turned and still look identical... This cross rotational symmetry of order 4. Have a go at the worksheets on congruence and symmetry....

Properties of quadrilaterals You need to know and be able to recognise these Now try the worksheet...

Polygons Polygons are many sided shapes – they can be or regular irregular Regular polygon worksheet

Angles in a polygon Do you remember the sum of the angles inside a triangle? 180° How do we work out the sum of the angles inside other polygons? We cut them up into triangles .... Each triangle adds to 180° and so 2 triangles must add to 360°. This means the INTERIOR angles of a quadrilateral add to 360°... Look at some more... This means that the sum of the interior angles for an n sided polygon is (n-2) x 180°

Angles in a polygon So far we have looked at INTERIOR angles These angles are called EXTERIOR angles. As you can see, they take you round in a circle. So the sum of the EXTERIOR angles of a polygon is 360°.

Angles in a polygon So if the shape is a REGULAR polygon, all the exterior angles are the same... So, for a pentagon, there are 5 identical exterior angles... And each one must be 360° ÷ 5 = 72°

Angles in a polygon And if the exterior angle is 72°, The INTERIOR one must be 180° - 72° = 108° (angles on a straight line)

Angles in a polygon Rules to remember: The sum of the exterior angles is 360° for any polygon. For regular polygons the exterior angle is 360° ÷ number of sides. For regular polygons the angle at the centre is also The interior angle + exterior angle = 180°. The sum of the interior angles is (n-2)x180° is for a polygon with n sides.

Angles in a polygon Try these: What is the sum of the interior angles of a polygon with 15 sides? What is the sum of the interior angles of a polygon with 20 sides? A regular polygon has 12 sides. What sizes are the interior and exterior angles? A regular polygon has 100 sides. What sizes are the interior and A regular polygon has an exterior angle of 24°. How many sides does it have? A regular polygon has an interior angle of 162°. How many sides Three of the four exterior angles of a quadrilateral are 94°, 50° and 85°. What’s the fourth exterior angle? How big are the interior angles?