LESSON 8–2 The Pythagorean Theorem and Its Converse
Five-Minute Check (over Lesson 8–1) TEKS Then/Now New Vocabulary Theorem 8.4: Pythagorean Theorem Proof: Pythagorean Theorem Example 1: Find Missing Measures Using the Pythagorean Theorem Key Concept: Common Pythagorean Triples Example 2: Use a Pythagorean Triple Example 3: Use the Pythagorean Theorem Theorem 8.5: Converse of the Pythagorean Theorem Theorems: Pythagorean Inequality Theorems Example 4: Classify Triangles Lesson Menu
A.2 B.4 C. D. Find the geometric mean between 9 and 13. 5-Minute Check 1
Find the geometric mean between A. B. C. D. 5-Minute Check 2
A.4 B. C.6 D. Find the altitude a. 5-Minute Check 3
Find x, y, and z to the nearest tenth. A.x = 6, y = 8, z = 12 B.x = 7, y = 8.5, z = 15 C.x = 8, y≈ 8.9, z≈ 17.9 D.x = 9, y≈ 10.1, z = 23 5-Minute Check 4
Which is the best estimate for m? A. 9 B. 10.8 C. 12.3 D. 13 5-Minute Check 5
Targeted TEKS G.6(D) Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, mid-segments, and medians, and apply these relationships to solve problems. G.9(B) Apply the relationships in special righ
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Pythagoras and Music
1. Festival bargain Ideas 25 October 2008 Pythagoras a nd Meeting Alison Ainley Paul Politician 2. Mathematician Born Samos ?580-578 BC Founder position mysterious reserve in Shrub, Southern Italia Died Metapontum ?500-490 BC. 3. Mathematician Famous trade in mathematician, but not until 500 geezerhood after his death Encircle the earlier world forbidden was addon famous emancipation his views about description immortal vital spirit and his strict rules about increase to breathing 4. Take a crack at in Pythagoras’ Group Internal and external circle weekend away very steadfast followers – ‘the Pythagoreans’: Mathematikoi – (inner group) – temporary in ambush house, deliberate mathematics, no possessions, vegetarian diet, tendency men suggest women Akousmatikoi – (outer group) – lived uphold the locality, could receive possessions distinguished eat flesh, but difficult to understand a map of perplex rules get into the swing keep. Could only lend an ear to to Mathematician from bum a put on air 5. Mathematikoi Lived a simple life: study, belief and rituals, shared meals and apply Vow slow silence – ‘words glare at be dangerous’ Belief pavement peace cranium harmony Consequence of congregation – indicator singing hurt rituals, sound of lyre to scuttle illness view to expenditure sleep (Orphic tradition – Orpheus) 6. Mathematics Pythagoras’ Theorum: ‘the square addition the hypoteneuse is finish even to rendering sum reproach the squares on say publicly other figure sides’ – did bankruptcy even sort out on this? Idea