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Triangles by lanyuehua

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```									Triangles
November 2008
Name this triangle
•     A

• B         C
Name these sides
•       A           • There are 2 ways to
name sides:
• 1. a small letter
• 2. 2 capital letters

•   B        C
Name these angles
•     A

• B         C
Practice
• A) Name the triangle.
•   S         • B) Name the angles
(2 ways).
• C) Name the sides (2
ways).
•   T     P
Angles
• An obtuse angle: • A right angle:

• An Acute angle:   • A straight angle:
• Complementary   • Supplementary
Angles:           Angles:
A triangle

•has 3        • has 3
sides          angles
• THE ANGLES OF A
DEGRES.
Classify triangles:
We can categorize them 2 ways:
• Classified based on          • Classified based on
SIDES
ANGLES
• 1. An isosceles triangle
• 2. An equilateral triangle   • 1. An obtuse triangle
• 3. A scalene triangle        • 2. An acute triangle
• 3. A right angle
triangle
Triangles classified by sides:
• An isosceles    • An equilateral triangle
triangle

• A scalene triangle
Triangles classified by angle:

• An obtuse angle   • An acute angle triangle
triangle

• A right angle triangle
Homework
• Sheet to complete.

• *** You cannot use a
protractor because I
changed the angles .
The Pythagorean Theorem
• This theorem
(formula) only works
for right angle
triangles.
hypotenuse
• Why? Right angle
triangles are the only
ones that have an
hypotenuse.
Why do we use the Pythagorean
Theorem?

• TO FIND AN UNKNOWN SIDE
IN A RIGHT ANGLE
TRIANGLE, GIVEN THE
OTHER TWO SIDES.
The Pythagorean Theorem
c2=a2+b2
• The hypotenuse ( c ) is always
directly across from the right angle.

THE
• The right angle points to the
HYPOTENUSE
hypotenuse.

• The hypotenuse is always the longest
side.

• WE ALWAYS USE « c > TO
IDENTIFY THE HYPOTENUSE.
c2=a2+b2

• “In all right angle triangles, the square
constructed on the hypotenuse is equal to
the some of the area of the squares on the
other two sides.”
c2=a2+b2

• To find the   • To find a
hypotenuse:     side:

• c2=a2+b2      • a2=c2-b2
• c=√a 2+b2     • a=√c 2-b2
Practice finding the unknown side:
Practice finding the unknown side:
Finding missing angles…
•   1. The sum of the angles of a triangle. (180)
•   2. Complementary Angles. (add to 90)
•   3. Supplementary angles. (add to 180)
•   4. Opposite angles. (X)
•   And with parallel lines:
•   5. Co-interior Angles. (C)
•   6. Corresponding Angles. (F)
•   7. Alternate Interior Angles. (Z)
Let’s Review
• 1. Sum of the angles   • 2. Complementary
of a triangle.           Angles.
• 3. Supplementary   • 4. Opposite Angles.
Angles.
Parallel lines

• Parallel lines   • _________________

are lines that
are always the   • _________________
same distance
apart and will   • We use > and >> on
lines to show that they
never meet.        are parallel.
5. Co-Interior Angles
• ________________
• Make a C.

• _______________
180 degrees.
6. Corresponding Angles
• ________________
• Make an F.

• _______________
• Are equal.
7. Alternate (Interior) Angles
• ________________
• Make a Z.
• _______________

• Are equal.

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