Mathematics Specification A - 4MA1 PearsonEdexcel

Similarity

Gbogbo ọrọ náà

Similar shapes are everywhere: a photograph and its enlargement, a model car and the real thing, a map and the landscape it represents. In each case the shape is the same but the size is different, and a single scale factor links every pair of corresponding lengths.

You will learn to identify similar figures, calculate unknown lengths using scale factors, and work with maps and scale drawings. At Higher tier, you will discover that areas scale by the square of the linear factor and volumes by the cube.

Ebumnobi

Understand and use the geometrical properties that similar figures have corresponding lengths in the same ratio but corresponding angles remain unchanged
Use and interpret maps and scale drawings
[Higher] Understand that areas of similar figures are in the ratio of the square of corresponding sides
[Higher] Understand that volumes of similar figures are in the ratio of the cube of corresponding sides
[Higher] Use areas and volumes of similar figures in solving problems

Akọmọ Ojú-ẹkọ

A passport photo enlarged to poster size keeps the same proportions but changes every length by the same multiplier. That multiplier is the scale factor, and it is the key to every similarity calculation.

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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Similarity. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

Two similar rectangles have lengths 5 cm and 20 cm. The scale factor is: A) 2 B) 4 C) 15 D) 100 Answer: B
If the scale factor of two similar shapes is 3, the area scale factor is: A) 3 B) 6 C) 9 D) 27 Answer: C
A map scale is 1:50 000. What does 4 cm on the map represent? A) 200 m B) 2 km C) 20 km D) 500 m Answer: B
Two similar solids have a volume ratio of 8:27. The linear scale factor is: A) 2:3 B) 4:9 C) 8:27 D) 3:2 Answer: A
Shapes are similar if: A) They have the same area B) They have the same perimeter C) Corresponding angles are equal and sides are proportional D) They have the same number of sides Answer: C