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
129 41 what's wrong with this? AutoSave 2
b 60 a c d e f 65 h i g 55 AutoSave 3
a b 163 c 70 d e AutoSave 4
Classify the angles; right, acute, or obtuse. 1 3 5 2 4 AutoSave 5
What is the definition for congruent? same size same shape answer AutoSave 6
Triangles 3 sided polygons AutoSave 7
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
A triangle with no congruent sides is a scalene triangle. 2 cm 4 cm 3 cm AutoSave 9
A triangle with all sides congruent is an equilateral triangle. 3 cm 3 cm 3 cm AutoSave 10
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
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
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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
A triangle that has three acute angles is an acute triangle. How else can we classify this triangle? AutoSave 15
A triangle that has one obtuse angle is an obtuse triangle. How else can we classify this triangle? AutoSave 16
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
Let's Practice Naming Triangles Acute Isosceles Right Isosceles Obtuse Isosceles AutoSave 18
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Sum of angles in Triangle AutoSave 20
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
Classify each triangle according to its angles right acute obtuse right acute obtuse AutoSave 22
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
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
3 Evaluate the expression A 10 B 36 C 20 D 64 = 4 + 16 = 20 click me AutoSave 25
4 Evaluate the expression A 24 B 74 = 49 + 25 = 74 click me C 18 D 144 AutoSave 26
5 Solve the equation. Check your answer. x + 13 = 37 A 50 B 13 C 24 D 37 x + 13 = 37 13 13 x = 24 Check step x + 13 = 37 24 + 13 = 37 37 = click 37 me AutoSave 27
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
Rational versus Irrational Square Roots All the other numbers between 1 256 are IRRATIONAL. AutoSave 29
Practice... AutoSave 30
Simplifying Radicals Number Systems What happens when you take the square root of a 'non perfect' square? Think... 20 is between what two perfect squares? What's the square root of 20? AutoSave 31
Simplifying Radicals Number Systems Estimate the root of a non perfect square. Since 20 is closer to 16, but more than 16... Estimate the root of 20 to be more than 4, but less than 5 4.4 20 is between 16 and 25. Closer to 16 AutoSave 32
Number Systems Pythagorean Theorem and Right Triangles REAL NATURAL WHOLE INTEGER RATIONAL IRRATIONAL AutoSave 33
Who is Pythagoras? Pythagoras was one of the first pure mathematicians from 500 B.C. time period. AutoSave 34
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
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More Pythagorean Puzzles AutoSave 37
Express the Pythagorean Theorem 2 2 2 + = AutoSave 38
For which triangles does the Pythagorean theorem apply? 1 2 3 4 5 AutoSave 39
Which of these two triangles are right triangles? a = 8 c = 12 b = 8 b = 12 c = 13 8 2 + 8 2 = 12 2 64 + 64 144 128 144 a = 5 12 2 + 5 2 = 13 2 144 + 25 = 169 169 = 169 AutoSave 40
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
Find the missing lengths 5 8 c y 6 Length of the hypotenuse a 2 + b 2 = c 2 8 2 + 6 2 = c 2 64 + 36 = 100 100 = c 2 c = 10 8 Length of a leg a 2 + b 2 = c 2 5 2 + y 2 = 8 2 25 + y 2 = 64 y 2 = 39 y = 6.2 AutoSave 42
What is the distance from A to B? (to the nearest mile) A North Dakota 210 m 340 m B 210 2 + 340 2 = 159,700 South Dakota Distance from A to B 400 miles AutoSave 43
How high off the ground is Ollie the owl? 43 ft 12 ft AutoSave 44
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
Pythagorean Theorem and Right Triangles Using the Pythagorean Theorem Example 2: Find the unknown measurement. Refer to the diagram. 15 12 AutoSave 46
Pythagorean Theorem and Right Triangles Using the Pythagorean Theorem 1) rewrite formula 2) substitute known quantities 3) use algebra to solve 4) check answer 3 5 4 AutoSave 47
Pythagorean Theorem and Right Triangles Using the Pythagorean Theorem Example 2: Find the unknown measurement. Refer to the diagram. 15 12 AutoSave 48
Question and "answer" on real test...and you wonder why teachers look so stressed some days... AutoSave 49
Pythagorean Triples 3 4 5 (and multiples of) 5 12 13 (and multiples of) 7 24 25 (and multiples of) AutoSave 50
? cm 10 cm Can you recognize the triple? 8 cm AutoSave 51
0.4 cm? cm 0.3 cm AutoSave 52
Find the diameter AutoSave 53
Find the diagonal AutoSave 54
Given this triangle, which of the following is similar but not congruent? AutoSave 55
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
Find the distance from Maple to Sable. AutoSave 57
Attachments pythagorean.notebook