PYTHAGORAS __ __ __ __ __
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
PYTHAGORAS
__ __ __ __ __
Find the message: A famous quotation of Pythagoras is given in the boxes. To find this, cross out the box that does illustrate a property of a right triangle. The remaining boxes will give the quotation.
1. WORLD 2. ABOVE 3. ALL 4. EXACT
It has parallel sides.
Its acute angles are
complementary.
The perpendicular sides are the
legs.
The interior angles are congruent.
5. THINGS 6. REVERENCE 7. CAPACITY 8. OF
If c is the hypotenuse,
then a2+b2=c2
Either legs of a right triangle
can serve as the altitude.
It has two right angles.
If two legs are congruent then all the angles
are congruent.9. OUR 10. TO 11.FUTURE 12. YOURSELF
The hypotenuse can be shorter to any of the
two legs.
The altitude is proportional to the segments of the hypotenuse.
The legs a and b can be opposite
to the right angle.
If two legs of a right triangle
are congruent, then it is a 45-45-90 triangle.
PYTHAGORASAbove all things,
reverence yourself.
RIGHT TRIANGLE SIMILARITYWAIT....What are the parts of a right triangle?
RECALL...E
IL
RIGHT TRIANGLE SIMILARITY
G
E L
M
I R
RATIO OF CORRESPONDING SIDESG
E L
M
I R
hypotenuse
opposite leg
adjacent leg
hypotenuse
opposite leg
adjacent leg
TRIGONOMETRIC RATIOS...
before that...What is trigonometry?
TRIGONOMETRYderived from the Greek words trigonon and metria, that means measurement of triangles.
Now lets go back...
TRIGONOMETRIC RATIOS
Let be a right triangle with right angle at E. The sine (sin), cosine (cos), and tangent (tan ) are defined as follows:
G
EL
GEL
sin L = = hypotenuse
Loppositeside c
a
cos L = = hypotenuse
Ltoadjacentside c
b
tan L = = Ltoadjacentside
Loppositeside
b
a
ca
b
CHECK YOUR UNDERSTANDING... G
E L
M
I R
51
45
24
1715
8
Compare the sine, cosine and tangent ratios for angles L and R in each triangle below.
EXAMPLE:M
I R
12
5
1. Find the value of sin M, cos M, and tan M in the figure below:
2. Using the same figure, find the value of sin R, cos R, and tan R.
SYNTHESIS: Help me make this
easy!
Let be a right triangle with right angle at E. The sine (sin), cosine (cos), and tangent (tan ) are defined as follows:
G
EL
GEL
sin L = = hypotenuse
Loppositeside c
a
cos L = = hypotenuse
Ltoadjacentside c
b
tan L = = Ltoadjacentside
Loppositeside
b
a
ca
b
sin L = = hypotenuse
Loppositeside c
a
cos L = = hypotenuse
Ltoadjacentside c
b
tan L = = Ltoadjacentside
Loppositeside
b
a
SOHCAHTOA
SOHCAHTOA
SOHCAHTOA
SOHCAHTOA
SOHCAHTOA
ASSIGNMENT:
Answer pp. 283 numbers 1-6 in your notebook.