Transformations & Angles
On your white board:
Sketch a ray.
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What does it mean when two things are congruent?
Same size, same shape.
What does SOH CAH TOA mean? Make sure to tell me what EVERY letter means.
SOH: Sine = opposite/hypotenuse
CAH: Cosine = adjacent/hypotenuse
TOA: Tangent = opposite/adjacent
What 3D shape has 2 triangular bases?
Triangular prism.
What is the equation of a circle?
(x-h)^2 + (y-k)^2 = r^2
Explain the difference between a translation, rotation, and reflection.
Translation: Slide, moves up/down, left/right
Rotation: Turn, turns 90 degrees, 180 degrees, 270 degrees.
Reflection: Flip, mirror over the line of reflection
What does it mean when 2 things are similar?
Same shape, different size.
When do you use inverse functions?
To find the angle.
What is the volume formula for a hemisphere?
((4/3)*pi*r^3)/2
Name the two most important characteristics of a circle.
The center and the radius.
Name two types of angles that are congruent.
Vertical angles
Corresponding angles
Alternate Interior angles
Name 2 triangle congruence theorems.
SSS congruence
SAS congruence
ASA congruence
AAS congruence
What trig function would you use to find the value of the angle if:
-hypotenuse = 15 inches
-opposite = 3 inches
Inverse sine
Find the volume of a cone:
radius = 12 cm
Height = 60 cm
2880pi cm^3
What is the equation of a circle with a center at (-3,-7) and a diameter of 18 inches?
(x+3)^2 + (y+7)^2 = 81
Look at the poster and find the value of x.
x=25 degrees
Reflexive property means that everything is congruent to itself.
Find the value of the opposite side if:
-reference angle = 61
-adjacent = 12 meters
Round to the nearest hundredth.
opposite side = 21.65 meters
Find the Height of the rectangular prism:
b=7 in
h=9 in
V=819 in^3
H = 13in
What is the equation of a circle with a center at the origin and a radius that passes through the point (10, 0)?
(x-0)^2 + (y-0)^2 =100
or
(x)^2 + (y)^2 =100
Look at the poster and find the value of k.
k=164 degrees
Given: The diagram.
Prove that triangle ABC ~ triangle DEC.
Remember to start your proof with the given and end the proof with a triangle similarity statement and the similarity theorem.
*You can write or say your proof.
Line segment AB is parallel to line segment DE->Given
Angle BCA is congruent to angle ECD->Vertical angles are congruent
Angle A is congruent to angle D->With parallel lines, alternate interior angles are congruent.
Triangle ABC ~ triangle DEC by AA~
*Could also use triangle sum theorem
*Could also use angle E congruent to angle B -> with parallel lines, alternate interior angles are congruent
Find the value of the hypotenuse if:
-reference angle = 34 degrees
-adjacent = 60 feet
Round to the nearest hundredth.
hypotenuse = 72.37 feet
Look at the poster, find the volume.
48 cm^3
What is the equation of a circle with a center at (4,-2) and a radius that passes through the point (10, -16)?
(x-4)^2 + (y+2)^2 =232