Geometry: Classifying, Identifying, and Constructing Triangles


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1 Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral triangles. 3) Classify acute, right, and obtuse triangles. 4) Classify scalene, isosceles, equilateral triangles. 5) Construct acute, right, and obtuse triangles. 6) Construct scalene, isosceles, equilateral triangles. AutoSave 1
2 what's wrong with this? AutoSave 2
3 b 60 a c d e f 65 h i g 55 AutoSave 3
4 a b 163 c 70 d e AutoSave 4
5 Classify the angles; right, acute, or obtuse AutoSave 5
6 What is the definition for congruent? same size same shape answer AutoSave 6
7 Triangles 3 sided polygons AutoSave 7
8 You can classify triangles by the lengths of their sides. 3 cm 3 cm A triangle with exactly two congruent sides is an isosceles triangle. 2 cm AutoSave 8
9 A triangle with no congruent sides is a scalene triangle. 2 cm 4 cm 3 cm AutoSave 9
10 A triangle with all sides congruent is an equilateral triangle. 3 cm 3 cm 3 cm AutoSave 10
11 Naming Triangles Names According To Side Lengths Equilateral  All three sides are the same length Isosceles  Two sides are the same length Scalene  No sides same length AutoSave 11
12 You can also classify triangles by the measures of the third angle...? A triangle that has a right angle is a right triangle. How else can we classify this triangle? AutoSave 12
13 AutoSave 13
14 Right Triangle leg hypotenuse The hypotenuse is the side opposite the right angle and is the longest side. leg The other sides are called legs. AutoSave 14
15 A triangle that has three acute angles is an acute triangle. How else can we classify this triangle? AutoSave 15
16 A triangle that has one obtuse angle is an obtuse triangle. How else can we classify this triangle? AutoSave 16
17 Naming Triangles Names According To Angles Right  Exactly 1 Right Angle and Two Acute Angles Acute  Three Acute Angles Obtuse  Exactly 1 Obtuse Angle and 2 Acute Angles AutoSave 17
18 Let's Practice Naming Triangles Acute Isosceles Right Isosceles Obtuse Isosceles AutoSave 18
19 AutoSave 19
20 Sum of angles in Triangle AutoSave 20
21 Classify each triangle according to its sides. 3 yd 6 ft 3 yd 3 yd 8 ft 4 ft 4 ft 5 ft 2 ft 1 in 3 in 3 in isosceles scalene scalene equilateral AutoSave 21
22 Classify each triangle according to its angles right acute obtuse right acute obtuse AutoSave 22
23 1 Refer to the graph on the right. The ordered pair for Point A is A (1, 3) B ( 1, 3) A C (1, 3) D ( 1, 3) +3 1 click me AutoSave 23
24 2 Refer to the graph on the right. The ordered pair for Point W is A (2, 4) B ( 4, 2) C (2, 4) +2 D (4, 2) 4 W click me AutoSave 24
25 3 Evaluate the expression A 10 B 36 C 20 D 64 = = 20 click me AutoSave 25
26 4 Evaluate the expression A 24 B 74 = = 74 click me C 18 D 144 AutoSave 26
27 5 Solve the equation. Check your answer. x + 13 = 37 A 50 B 13 C 24 D 37 x + 13 = x = 24 Check step x + 13 = = = click 37 me AutoSave 27
28 Radical Man! Known as the Radical symbol. It can also be called "square root"... is read, "What times itself is 25?" or "What value when squared is 25?" Recall: 5² is 25 so... = 5 AutoSave 28
29 Rational versus Irrational Square Roots All the other numbers between are IRRATIONAL. AutoSave 29
30 Practice... AutoSave 30
31 Simplifying Radicals Number Systems What happens when you take the square root of a 'non perfect' square? Think is between what two perfect squares? What's the square root of 20? AutoSave 31
32 Simplifying Radicals Number Systems Estimate the root of a non perfect square. Since 20 is closer to 16, but more than Estimate the root of 20 to be more than 4, but less than is between 16 and 25. Closer to 16 AutoSave 32
33 Number Systems Pythagorean Theorem and Right Triangles REAL NATURAL WHOLE INTEGER RATIONAL IRRATIONAL AutoSave 33
34 Who is Pythagoras? Pythagoras was one of the first pure mathematicians from 500 B.C. time period. AutoSave 34
35 Sort the keywords. Word Description The sides of a right triangle that share the 90 degree angle. The side of a right triangle that is opposite the 90 degree angle. The sum of the squares of the legs is equal to the square of the hypotenuse. Hypotenuse a 2 Right Coordinate + Legs Triangle Label b 2 = c 2 Plane AutoSave 35
36 AutoSave 36
37 More Pythagorean Puzzles AutoSave 37
38 Express the Pythagorean Theorem = AutoSave 38
39 For which triangles does the Pythagorean theorem apply? AutoSave 39
40 Which of these two triangles are right triangles? a = 8 c = 12 b = 8 b = 12 c = = a = = = = 169 AutoSave 40
41 Identify the legs and the hypotenuse legs hypotenuse b a c z y j k x l a b c a c b z y x j l k AutoSave 41
42 Find the missing lengths 5 8 c y 6 Length of the hypotenuse a 2 + b 2 = c = c = = c 2 c = 10 8 Length of a leg a 2 + b 2 = c y 2 = y 2 = 64 y 2 = 39 y = 6.2 AutoSave 42
43 What is the distance from A to B? (to the nearest mile) A North Dakota 210 m 340 m B = 159,700 South Dakota Distance from A to B 400 miles AutoSave 43
44 How high off the ground is Ollie the owl? 43 ft 12 ft AutoSave 44
45 Find the length of the diagonal of the base of this prism (AC) 4 cm 15 cm 10 cm Then find the length of AG AutoSave 45
46 Pythagorean Theorem and Right Triangles Using the Pythagorean Theorem Example 2: Find the unknown measurement. Refer to the diagram AutoSave 46
47 Pythagorean Theorem and Right Triangles Using the Pythagorean Theorem 1) rewrite formula 2) substitute known quantities 3) use algebra to solve 4) check answer AutoSave 47
48 Pythagorean Theorem and Right Triangles Using the Pythagorean Theorem Example 2: Find the unknown measurement. Refer to the diagram AutoSave 48
49 Question and "answer" on real test...and you wonder why teachers look so stressed some days... AutoSave 49
50 Pythagorean Triples (and multiples of) (and multiples of) (and multiples of) AutoSave 50
51 ? cm 10 cm Can you recognize the triple? 8 cm AutoSave 51
52 0.4 cm? cm 0.3 cm AutoSave 52
53 Find the diameter AutoSave 53
54 Find the diagonal AutoSave 54
55 Given this triangle, which of the following is similar but not congruent? AutoSave 55
56 What is the length, in units, of line segment AC? Show or explain how you got your answer. What is the area, in square units, of triangle ABC? Show or explain how you got your answer. In your Student Answer Booklet, draw a rectangle that has the same area in square units as triangle ABC. Be sure to label the dimensions of your rectangle. AutoSave 56
57 Find the distance from Maple to Sable. AutoSave 57
58 Attachments pythagorean.notebook
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