Transformations
What is the name of the transformation where you make shapes bigger or smaller?
Dilation
Complementary Angles
What kind of polygon can the pythagorean theorem be used on?
Sine (sin=opp/hyp)
Cosine (cos=adj/hyp)
Tangent (tan=opp/adj)
Angle A = 40 degrees & Angle B is the right angle
Your hypotenuse length is 5 inches and one of your legs is 4 inches.
A^2 + 16 = 25 --> A^2 = 9 --> A = 3
Then 90 + 40 = 130 and 180 - 130 = 50 degrees for angle C
When you translate a polygon, is the pre-image congruent to the image?
Yes
What is the name of the theorem that states that two angles on opposite sides of two intersecting lines are congruent? Draw and label a pair on your whiteboard
Vertical Angles Theorem
Can a right triangle with side lengths of 3, 4, and 9 exist?
No
Given an equation where you are solving for an angle θ, what are the three options for the operation you could be asked to use?
arcsine, arccosine, arctangent
If you make a right triangle with the angle of elevation and angle of depression in a particular scenario, are those two triangles similar?
Yes! Because the angles are congruent
Which transformations have coordinate rules that involve flipping the x and y coordinates of the vertices of a polygon?
Reflections and Rotations
If you know the value of one angle in an isosceles triangle, can you determine the other two angles?
Yes, using the base angles theorem
Can a right triangle with side lengths 7, 9 and the square root of 130 exist?
Yes!
On your whiteboard, label the sides of a right triangle (opposite, adjacent, hypotenuse) in relation to an angle θ (you can choose the angle).
See whiteboard
In an isosceles right triangle, what is the measure of each of the angles? And, given that the hypotenuse length is 4 inches, what is the length of the legs of the triangle?
45, 90, 45 degrees
2x^2 = 4^2 --> 2x^2 = 16 --> x^2 = 8
leg length would be the square root of 8 (2.83)
If triangle ABC has vertices at (1, 5) (4, 4) and (2, 1), what will the vertices of it's reflected image A'B'C' be after being flipped over the y axis?
(-1, 5) (-4, 4) (-2, 1)
What does the corresponding angles theorem state. Draw an example of corresponding angles in a transversal diagram on your whiteboard.
Angles in the same part of congruent but separate figures are congruent
A right triangle has leg lengths of 9.5 in and 7 in. What is the length of the hypotenuse? Round to the nearest 100th in
11.80 in
In an equation involving an angle of elevation of 35 degree where you are solving for the height of a building being viewed from 20 feet away, what trigonometric operation will you use?
Tangent (tan(35))
Given a right triangle with an acute angle of 35 degrees and an opposite leg length of 4 inches, find the other sides and angle measurements.
final angle is 55 degrees.
sin (35) = 4/x --> .5736 = 4/x --> x = 6.974 inches for the hypotenuse
tan (35) = 4/x --> .7002 = 4/x --> x = 5.713 inches for the other leg
Point A is currently at (5, 7), and is rotated around the origin by 90 degrees counter-clockwise to create image A'. What are the coordinates of A'?
(-7, 5)
Right triangle ABC ~ DEF. Given that angle A = 45°, what are the two options for the measure of angle F?
45° or 90°
A right triangle has hypotenuse length 12 and one leg with side length 6. What is the measure of the other leg? Round to the nearest 100th.
10.39 or square root of 108
Write and solve an equation for the following:
You are building a play structure and you need to design a slide. The ledge you want to connect your slide to is 10 feet up and the angle of elevation you need your slide to be inclined at to meet safety regulations is 35 degrees. How long of a slide do you need?
sin(35) = 10/x
0.5736 = 10/x
0.5736x = 10
x = 17.433
The slide must be 17.433 feet
Correctly solve a problem created by the other team (double points)!
See other team