Lecture notes, lecture USEFUL FACTS ABOUT ANGLES PDF

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USEFUL FACTS ABOUT ANGLES By the Maths Learning Centre, University of Adelaide

The Basics 𝛾

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Angles on a line add to 180°.

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Angles at a point add to 360°.

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When two lines cross, opposite angles are equal.

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Parallel Lines 𝛼

When a line crosses parallel lines, alternate angles are equal.

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When a line crosses parallel lines, corresponding angles are equal.

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When a line crosses parallel lines, co-interior angles add to 180°.

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Shapes 𝛽

The angles in any triangle add to 180°. 𝛼

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The angles in any quadrilateral add to 360°.

The angles in any polygon with ) to ( .

sides add

Angle sum

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USEFUL FACTS ABOUT ANGLES By the Maths Learning Centre, University of Adelaide

Triangles 𝛼

The angles in any triangle add to 180°.

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In a right-angled triangle, the two smaller angles add to 90°.

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

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𝛾 𝑎

In an isosceles triangle (two sides equal), the angles opposite the equal sides are equal.

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60°

In an equilateral triangle (all sides equal), the angles are all 60°.

60°

60°

Circles 𝛼

In a circle, all the angles subtended at the edge by the same chord are equal.

In a circle, the angle subtended at the centre by a chord is twice the angle subtended at the edge.

The angle in a semicircle is a right angle.

At a point on the edge of a circle, the angle between the radius and the tangent is a right angle.

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