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Geometry — NUET тақырыптар | StudyWithRaissov | StudyWithRaissov

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Математика28 мин

Geometry

Core geometry: angle facts, parallel-line theorems, similarity, and the area/volume zoo.

Тәжірибе

01

Angle facts

Angles on a straight line sum to 180°.
Angles around a point sum to 360°.
Vertically opposite angles are equal.
Parallel lines: corresponding equal, alternate equal, co-interior sum to 180°.

02

Area cheatsheet

Shape	Area
Triangle	$\tfrac{1}{2}bh$
Parallelogram	$bh$
Trapezium	$\tfrac{1}{2}(a+b)h$
Circle	$\pi r^2$
Sector ( $\theta$ rad)	$\tfrac{1}{2}r^2\theta$

03

Similarity and scale

Similar figures have equal angles and proportional sides. If linear scale is $k$ , areas scale by $k^2$ and volumes by $k^3$ .

Жаттығу

A triangle with sides 3, 4, 5 is similar to one with sides 9, 12, 15. Ratio of areas?

Жауап пен түсініктемені көру

Жауап: 1 : 9

Linear scale 3, area scale $3^2 = 9$ .

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