Geometry: Classifying, Identifying, and Constructing Triangles

Transcription

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