Right
Triangles and Special Triangles
Now that you know about Acute
and Obtuse Triangles, you can learn about:
Right
Triangles
You
are going to use a neat program to explore right triangles. The instructions
below will guide you and allow you to find out what a right triangle is!
Construct
a line, l1
Construct
a line, l2, perpendicular to the original line
(remember when
one line is perpendicular to another, they form a right angle. A
"right angle" is a 90 degree angle and looks like a perfect corner!)
Place
one point on line l1 and one point on l2
Label
these points, a and b, respectively
Connect
a and b with a segment
The
resulting figure is a right triangle!!
The
figure is a right triangle because there exists a right angle between two
of the sides of the triangle.
Move
point a on l1
Move
point b on l2
Even
though you are moving the points and changing the lengths of the sides
of the triangle, you are NOT changing the RIGHT angle between l1 and l2.
So,
every triangle you form with this sketch is a right triangle!!
Remember,
A right
triangle is a triangle with ONE right angle!
It's
as Simple as That---Right On!
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to the Top
Special
Triangles
I
have a puzzle for you...
It
is clear to see that by drawing a diagonal AC, that the square is divided
into 2 right triangles.
-
1.
How does that affect angle measures ACB, ACD, CAB, CAD?
-
2.
Can you find the length AC?
-
(HINT!! Use the Pythagorean
Theorem)
-
3.
Remembering that Sin of an angle is defined as opposite/hypotenuse,
What
is Sin 45?
You have
just worked with a special triangle called a 45-45-90 triangle. This
means that the triangle is a right triangle with the other angles equalling
45 degrees each!
When
you encounter this isosceles triangle, you can count on the fact that
hypotenuse
of the triangle is always: (the square root of two divided by two) multiplied
times the length of one of the legs of the triangle!
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to the Top
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