The ratio of the corresponding sides is equal A′B′ = B′C′ = A′C′ =k AB BC AC k is the scale factor. Similar Triangles Two triangles are similar if one of the following conditions holds: 1.The corresponding angles in the triangles are equal A = A′, B = B′, C = C′ 2. Solution: 8.62 = y2 + 5.62 y2 = 8.62 - 5.62 y = √( 8.62 - 5.62) y = 6.53cm Similar figures Shapes are similar when they have the same shape but not the same size. Solution: x2 = 5.32 + 6.12 √x2 = √(5.32 + 6.12) x = 8.08cmĮxample 2: Find the value, correct to two decimal places, of the unknown length for the triangle below. Solution Use the formula x°= (180n-360)° x°= 180×8-360 = 1080 ° Pythagoras theorem Example 1: Find the value, correct to two decimal places, of the unknown length for the triangle below. Solution ax = 360°÷ 8 = 45° b BOC is isosceles ∧ ∧ then OBC and OCB are equal x° + 2y°= 180° 45° + 2y° = 180° 2y°= 180° - 45° 2y°= 135° y° = 67.5°Įxample:Find the sum of the interior angles of an 8-sided polygon(octagon). Example1: The diagram opposite shows a regular octagon. The angle sum of the interior angles of an n-sided polygon is given by the formula: S = ◦ = (180n − 360)◦ The magnitude of each of the interior angles of an n-sided polygon is given by: x = (180n − 360)◦ n interior angle exterior angle The sum of the exterior angles of a regular polygon is 360◦. A polygon with n sides can be divided into n triangles. Properties of regular polygons A regular polygon has all sides of equal length and all angles of equal magnitude. The sum of the magnitudes of the exterior angles of a triangle is equal to 360°: e° +d°+f°=360° Example 1: Find the values of the pronumerals. If a triangle is isosceles, the angles opposite each of the equal sides are equal. A triangle is said to be isosceles if it has two sides of equal length. Ħ.The bisector of each of the angles of an equilateral triangle meets the opposite side at right angles and passes through the midpoint of that side. The angles of an equilateral triangle are all of magnitude 60◦. A triangle is said to be equilateral if all its sides are of the same length: AB = BC = CA. The magnitude of an exterior angle is equal to the sum of the magnitudes of the two opposite interior angles. The sum of the magnitudes of the interior angles of a triangle is equal to a ◦ + b◦ + c◦ = 180°. A triangle is said to be a right-angled triangle if it has one angle of magnitude 90°. d° is the magnitude of an exterior angle at C. a °, b° and c° are the magnitudes of the interior angles of the triangle ABC. Cointerior angles are supplementary (180∘).Įxample:Find the values of the pronumerals. The angles 3-6 and 4-5 are cointerior angles. The angles 3-4 and 4-6 are alternate angles. The angles 2-6, 1-5, 7-3 and 8-4 are corresponding angles.
Properties of parallel lines The angles 1-3, 2-4, 6-8 and 5-7 are vertically opposite angles.
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