Pythagoras, Similarity And Congruence
Akopọ
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.
Awọn Afojusun
- 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
Akọ̀wé Ẹ̀kọ́
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Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Pythagoras, Similarity And Congruence. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- 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
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
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Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Pythagoras, Similarity And Congruence? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
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