Pythagoras, Similarity And Congruence
Bayani Gaba-gaba
Three ideas do most of the heavy lifting in 4MB1 geometry: a right-angled triangle's sides obey a fixed relationship, enlarged shapes scale their area and volume in predictable ways, and two triangles can be proved identical using surprisingly little information. This topic ties all three together, because a similarity or congruence argument almost always ends with a Pythagoras calculation, or starts from one.
You will extend Pythagoras' theorem from flat diagrams into three-dimensional solids, learn why area scales by the square of the length scale factor and volume by its cube, and work through each of the four ways Edexcel accepts as proof that two triangles are congruent: SSS, SAS, ASA and RHS. Knowing exactly which condition applies, and being able to write the proof out fully, is worth real marks on both papers.
Manufura
- Use Pythagoras' theorem in 2D and 3D
- Understand and use similarity, including how scale factors relate to areas and volumes of similar figures
- Prove the similarity of two triangles
- Understand and identify congruent shapes
- Use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles
Taswirar tunani
An zana wannan batu don ka ga yadda ra'ayoyi ke hadewa.
Bude taswirar tunani a cikin manhaja
Katunan tunawa
Gwaji mai sauri kan abin da ake jarraba a wannan batu.
Yi atisayen wadannan katuna a cikin manhaja
Takardar Darasi
Cikakken Bayanin Darasi Yana Kan Manhajar Green Bridge
Sami manhajar Green Bridge CBT a wayarka ko kwamfutarka domin cikakken laburaren IGCSE: takardun jarrabawar baya, tsarin kimantawa, taswirar tunani, katunan karatu da darussan sauti.
Nazarin Darasi
Barka da kammala darasi akan Pythagoras, Similarity And Congruence. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- A right-angled triangle has shorter sides of 6 cm and 8 cm. What is the length of the hypotenuse? A) 7 cm B) 10 cm C) 14 cm D) 48 cm Answer: B
- A cuboid has edges 2 cm, 3 cm and 6 cm. What is the length of its space diagonal? A) 6 cm B) 7 cm C) 11 cm D) 49 cm Answer: B
- Two similar solids have a linear scale factor of 3. By what factor does the volume of the larger solid exceed the smaller? A) 3 B) 6 C) 9 D) 27 Answer: D
- Which condition CANNOT be used on its own to prove two triangles are congruent? A) SSS B) SAS C) SSA (side, side, non-included angle) D) RHS Answer: C
- Two right-angled triangles have equal hypotenuses and one further pair of equal corresponding sides. Which congruence condition proves they are congruent? A) AAS B) SSA C) RHS D) AA Answer: C
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
Use Properties of Angles, Triangles, and the Pythagorean Theorem
Use the properties of angles
"Prealgebra: Use Properties of Angles, Triangles, and the Pythagorean Theorem" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/prealgebra/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem. Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
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Sashen littafi
Solve Proportion and Similar Figure Applications
Solve proportions
"Elementary Algebra: Solve Proportion and Similar Figure Applications" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/elementary-algebra/pages/8-7-solve-proportion-and-similar-figure-applications. Access for free at https://openstax.org/books/elementary-algebra/pages/1-introduction
Wasu ƙungiyoyi ne suka wallafa su ƙarƙashin lasisin buɗe, kuma muna ambaton su yadda suka nema. Hanyoyin suna buɗe shafukansu.
Yi Aikin Tambayoyin Gwaji
Kana son yin aikin tambayoyin gwaji kan Pythagoras, Similarity And Congruence? Sauke manhajar Green Bridge CBT don samun tambayoyin gwaji da cikakkun jarrabawa akan wannan batu.
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