4th Hr' Geometry Week of 111609

1
4th Hr. GeometryWeek of 11/16/09

• Noreen Habana
• North Huron Schools

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Warm Up

• Simplify the following

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Orthocenter of a Triangle

• The point of intersection of the altitudes of a
  triangle is called the orthocenter.
• In the figure, AD, BE, and CF are the altitudes
  drawn from the vertices A, B, and C respectively.
  The point of intersection of these altitudes is
  H. So, H is the orthocenter of triangle ABC.

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Orthocenter of an Obtuse Triangle

• Orthocenter of an obtuse triangle
• lies outside the triangle.

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Orthocenter of an Acute Triangle

• Orthocenter of an acute triangle lies inside the
  triangle.

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Orthocenter of a Right Triangle

• Orthocenter of a right triangle lies on the
  triangle.

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Additional Practice

• In your notebook, work out p.259
  1-4,8,9,11,14-16.

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HW5.3 12,13,17,18,20,22,27-29,32

• On a separate sheet of paper, do pp.260-261
  12,13,17,18,20,22,27-29,32.
• Use 2 column format.
• Show work or explain answers for each problem.
• Due Tue. 11/17.

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Warm Up

• Simplify each expression. (Review on p.355)

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Circumscribe a triangle

• http//www.mathopenref.com/constcircumcircle.html

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Inscribe in a triangle

• http//www.mathopenref.com/constincircle.html

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Pythagorean Theorem Demo

• Draw a rectangle. Measure in cm and label its
  dimensions. Draw and measure in cm its diagonal.

• Draw a square with dimensions equal to the
  rectangles width.

• Draw a square with dimensions equal to the
  rectangles length.

• Draw a square with dimension equal to the
  rectangles diagonal length.

Add the area of the 2 smaller squares and compare
to the area of the larger square.
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NotesSect.7.2 The Pythagorean Theorem and its
Converse

• In a right triangle, a² b² c², where a and b
  are the lengths of the legs of the triangle and c
  is the length of the its hypotenuse.

c
a
b
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Example 1 of Sect.7.2

• Find the length of the hypotenuse of ?ABC.
• Solution

c
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Pythagorean Triple

• A Pythagorean triple is a set of nonzero whole
  numbers a,b, and c that satisfy the equation a²
  b² c².
• Example 3,4,5
• 3² 4² 5² 9 16 25
• Nonexample 2,3,4
• 2² 3² ? 4² 4 9 ? 16
• 2² 3² 13 0R

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Example 1 of Sect.7.2

• Do the length of ?ABC form a Pythagorean triple?
• Solution Since c 29,
• the lengths of the sides 20,
• 21, and 29 form a Pythagorean
• triple because they are whole
• numbers that satisfy a² b² c².

c
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Example 2 of Sect.7.2

• Find the value of x. Leave your answer in the
  simplest radical form.
• Solution

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Example 3 of sect.7.2

• How far is it to paddle from one dock to the
  other?
• Solution

350m
250m
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Circumscribe a triangle

• http//www.mathopenref.com/constcircumcircle.html

20
Inscribe in a triangle

• http//www.mathopenref.com/constincircle.html

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Pythagorean Theorem Demo

• Draw a rectangle. Measure in cm and label its
  dimensions. Draw and measure in cm its diagonal.

• Draw a square with dimensions equal to the
  rectangles width.

• Draw a square with dimensions equal to the
  rectangles length.

• Draw a square with dimension equal to the
  rectangles diagonal length.

Add the area of the 2 smaller squares and compare
to the area of the larger square.
22
NotesSect.7.2 The Pythagorean Theorem and its
Converse

• In a right triangle, a² b² c², where a and b
  are the lengths of the legs of the triangle and c
  is the length of the its hypotenuse.

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Example 1 of Sect.7.2

• Find the length of the hypotenuse of ?ABC.
• Solution

c
24
Warm Up

• In your notebook, work out p.355 5-9. Show
  work.

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Pythagorean Triple

• A Pythagorean triple is a set of nonzero whole
  numbers a,b, and c that satisfy the equation a²
  b² c².
• Example 3,4,5
• 3² 4² 5² 9 16 25
• Nonexample 2,3,4
• 2² 3² ? 4² 4 9 ? 16
• 2² 3² 13 0R

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Example 1 of Sect.7.2

• Do the length of ?ABC form a Pythagorean triple?
• Solution Since c 29,
• the lengths of the sides 20,
• 21, and 29 form a Pythagorean
• triple because they are whole
• numbers that satisfy a² b² c².

c
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Example 2 of Sect.7.2

• Find the value of x. Leave your answer in the
  simplest radical form.
• Solution

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Example 3 of sect.7.2

• How far is it to paddle from one dock to the
  other?
• Solution

350m
250m
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Example 4 of sect.7.2

• Find the area of the triangle.
• Solution

12m
12m
h
20m
30
Ex.4 continued
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Converse of Pythagorean Theorem

• A) If a² b² c², then triangle is a right
  triangle.
• B) If a² b² lt c², then triangle is an obtuse
  triangle.
• C) If a² b² gt c², then triangle is an acute
  triangle.

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Example 5 of Sect.7.2

• Is a triangle with sides 13,84, and 85 a right
  triangle?

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Example 6 of sect.7.2

• A) Classify the triangle with sides 6,11,14.

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Example 6 continued

• B) Classify the triangle with sides 12,13,15.

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Check Understanding 7.2

• In your notebook, do check understanding for
  section 7.2 (pp.357-360) 1-6.
• Use 2-column format.
• Show work for or explain each solution.
• Due Thur. 11/19.

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Warm Up

• In your notebook, work out p.355 20-24. Show
  work.

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HW 7.2 13,14,16,17,19,20,29-31,38

• On a separate sheet of paper, do pp.361-362
  13,14,16,17,19,20,29-31,38.
• Use 2 column format.
• Show work for or explain each solution.
• Due Fri.11/20.

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Sect. 7.3 Special Right Triangles

• Draw an isosceles right triangle.
• Label the legs, x.
• Label the hypotenuse, y.
• Use Pythagorean Theorem to find the relationship
  between legs and hypotenuse of an isosceles right
  triangle (45?-45?-90?).

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Notes Sect. 7.3 Special Right Triangle

• 45?-45?-90? Triangle Theorem
• In a 45?-45?-90? triangle, the legs are congruent
  to each other, and the hypotenuse is times
  the length of a leg.
• Hypotenuse leg

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Example 1 of sect.7.3

• A) Find the value of h.
• Since this is a 45?-45?-90? triangle and h is the
  hypotenuse, then .

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45?
45?
h
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Example 1 continued
45?

• Find the value of x.
• Since this is a 45?-45?-90? triangle and x is the
  hypotenuse, then

2
x
45?
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Sect. 7.3 Special Right Triangles

• Draw an equilateral triangle.
• Label the sides, x.
• Draw a perpendicular bisector from the base of
  the triangle, and label it h.
• Focus on just half of this triangle
  (30?-60?-90?). Use Pythagorean Theorem to find
  the relationship between its legs and hypotenuse.

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Notes Sect.7.3 Special Right Triangles
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Notes Sect. 7.3 Special Right Triangle

• 30?-60?-90? Triangle Theorem
• In a 30?-60?-90? triangle,
• Hypotenuse 2 short leg
• Long leg short leg x

30?
2s
s
60?
s
45
Example 4 of sect.7.3

• Find the value of each variable.

y
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Example 5 of sect.7.3

• Find the value of each variable.

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Example 6 of sect.7.3

• Find the area of an equilateral triangle.

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Additional Practice

• P.369 2-5,12,15-18,21,22,24,25,34,37

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Check Understanding 7.3

• In your notebook, work out check understanding
  (pp.366-369)1-6.
• Use 2-column format.
• Show work or explain work for each problem.
• Due Fri.11/20.