Pythagoras, Similarity And Congruence
Muhtasari
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.
Malengo
- 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
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Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- 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
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Vitabu Vinavyopendekezwa
Jifunze zaidi kutoka vyanzo huria
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Sehemu ya kitabu
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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Sehemu ya kitabu
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
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