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Flashcards · 4024 · Topic 4

Geometry flashcards

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Topic 4: Geometry

Similar and congruent shapes
Similar: same shape, with lengths in a constant ratio. Congruent: same shape and same size.
Sector and segment of a circle
Sector: bounded by two radii and an arc. Segment: bounded by a chord and an arc.
Bearings: the rules, and the back bearing of 296°
Measured clockwise from north, written with three figures (for example 040°). Back bearing: add 180° if under 180°, subtract 180° if 180° or more. 296° − 180° = 116°.
Similar shapes: length scale factor k. What are the area and volume scale factors?
Area scale factor k². Volume scale factor k³. Given areas or volumes, take the square root or cube root first to get k.
Two similar cylinders have heights in the ratio 2 : 3. The smaller holds 40 cm³. Find the volume of the larger.
Volume factor (3/2)³ = 27/8. 40 × 27/8 = 135 cm³.
Sum of the interior angles of a polygon with n sides
(n − 2) × 180°. The exterior angles of any polygon add up to 360°.
Each interior angle of a regular polygon is 140°. How many sides?
Exterior angle = 180° − 140° = 40°. n = 360° ÷ 40° = 9 sides.
Angles with parallel lines: corresponding, alternate, co-interior
Corresponding angles (F shape) are equal. Alternate angles (Z shape) are equal. Co-interior angles (C shape) add up to 180°.
Circle theorems: angle at the centre, and angle in a semicircle
The angle at the centre is twice the angle at the circumference standing on the same arc. The angle in a semicircle is 90°.
Circle theorems: cyclic quadrilateral, and angles in the same segment
Opposite angles of a cyclic quadrilateral add up to 180°. Angles in the same segment are equal.
Circle theorems about tangents
A tangent is perpendicular to the radius at the point of contact. Tangents from an external point are equal in length. Alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment.
A circle has diameter 26 cm. A chord is 10 cm long. How far is the chord from the centre?
The perpendicular from the centre bisects the chord. Radius 13, half-chord 5. Distance = √(13² − 5²) = √144 = 12 cm.

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