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Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 5.2
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Exercise 123 Page 304

Practice makes perfect
a An equilateral triangle has three congruent angles, each of them being 60^(∘).

However, we can also have triangles where only one angle is 60^(∘) and the others are something else.

Therefore, the conjecture is false.

b When calculating the area of a parallelogram you multiply its base and height. However, there are more shapes than parallelograms — for example, triangles and trapezoids. These do not follow this formula.

Therefore, the conjecture is false.

c If you rotate something 360^(∘) it ends up where it started. Let's show this with an arbitrary polygon.


Therefore, a shape can have any look and will have a 360^(∘) rotation symmetry, and the conjecture is true.

Subchapter links expand_more
arrow_right 5.2.1 Perfect Square Equations p.285-286
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68
Perfect Square Equations 69 (Page 285)
Perfect Square Equations 70 (Page 286)
arrow_right 5.2.2 Completing the Square p.289
Completing the Square 77 (Page 289)
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Completing the Square 79 (Page 289)
Completing the Square 80 (Page 289)
Completing the Square 81 (Page 289)
Completing the Square 82 (Page 289)
arrow_right 5.2.3 More Completing the Square p.291-292
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More Completing the Square 90 (Page 291)
More Completing the Square 91 (Page 292)
More Completing the Square 92 (Page 292)
More Completing the Square 93 (Page 292)
More Completing the Square 94 (Page 292)
arrow_right 5.2.4 Introduction to the Quadratic Formula p.296-297
Introduction to the Quadratic Formula 100 (Page 296)
Introduction to the Quadratic Formula 101 (Page 296)
Introduction to the Quadratic Formula 102 (Page 296)
Introduction to the Quadratic Formula 103 (Page 296)
Introduction to the Quadratic Formula 104 (Page 297)
Introduction to the Quadratic Formula 105 (Page 297)
arrow_right 5.2.5 Solving and Applying Quadratic Equations p.301-304
Solving and Applying Quadratic Equations 112 (Page 301)
Solving and Applying Quadratic Equations 113 (Page 301)
Solving and Applying Quadratic Equations 114 (Page 302)
Solving and Applying Quadratic Equations 115 (Page 302)
Solving and Applying Quadratic Equations 116 (Page 302)
Solving and Applying Quadratic Equations 117 (Page 303)
Solving and Applying Quadratic Equations 118 (Page 303)
Solving and Applying Quadratic Equations 119 (Page 303)
Solving and Applying Quadratic Equations 120 (Page 303)
Solving and Applying Quadratic Equations 121 (Page 303)
Solving and Applying Quadratic Equations 122 (Page 304)
Solving and Applying Quadratic Equations 123 (Page 304)
arrow_right 5.2.6 Introducing Complex Numbers p.308-310
Introducing Complex Numbers 131 (Page 308)
Introducing Complex Numbers 132 (Page 308)
Introducing Complex Numbers 133 (Page 309)
Introducing Complex Numbers 134 (Page 310)
Introducing Complex Numbers 135 (Page 310)
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