Unit 1: Tools of Geometry
What does it mean for two lines to be parallel? (2 part answer)
1) The lines have the same slope
2) The lines will never intersect
What is the key feature of an isosceles triangle?
(Bonus 50 points to the team that can name an alternative key feature!)
2 congruent sides (or 2 congruent angles)
What is standard form equation of a circle and why is it our ideal circle equation?
(x-h)2+(y-k)2=r2 and we LOVE it because it makes it easy to find the center and radius of any given circle.
Name me 3 key properties of a parallelogram.
(Bonus 50 points to the other team that can name the other 2!)
1) Opposite sides are congruent
2) Opposite sides are parallel
3) Opposite angles are congruent
4) Consecutive angles are supplementary
5) Diagonals bisect one another
What are the key ingredients of a rotation?
Center of rotation
Angle measure
Direction
What does it mean for two lines to be perpendicular? (2 part answer)
1) Their slopes will be negative reciprocals of each other
2) They intersect at a ninety degree angle
What does it mean for two triangles to be similar? Is it the same as when they are congruent and why?
100 points to any other team that can name A L L four triangle congruency patterns
When two triangles are similar, their corresponding sides are all proportional by the same scale factor but the corresponding angles remain congruent. If the two triangles are congruent, then the corresponding sides are the same length.
What is the center and radius of the circle whose equation is represented by (x-8)2+(y+9)2 = 36?
Center: (8, -9)
Radius: 6 units
Given a regular pentagon that is rotated about its center, find 3 angles of rotations that will map the figure onto itself.
72 degrees,
144 degrees,
216 degrees,
288 degrees,
360 degrees.
Under what condition can a dilation be considered a rigid motion? Why?
A dilation can be considered a rigid motion when the scale factor is 1 because this will preserve the distance between the vertices so that the image is congruent to the image.
What is the circumference of a circle whose area is 100pi square inches?
20pi inches
If sin x = 12/13 and cos x = 5/13, then tan x = ?
12/5
What is 120 degrees in radians? (Keep answer in terms of pi)
(2pi)/3 = (2/3)pi
What mathematical evidence do I need to prove that a quadrilateral has parallel opposite sides?
Need to find slope of each side to see if the opposite sides have the same slope.
I translate Point A(6, 22) to Point B(2, 18). How can I express this transformation in translation notation?
T-4, -4
In the figure on Slide 106, if the measure of angle Z = 2X + 28, what is the measure of angle Z?
92 degrees
The triangles in Slide 108 are similar. Find the value of x.
57 degrees
Consider the circle on Slide 113 with center at point O. What is the length of arc AB to the nearest tenth of a unit?
12.6 units
In parallelogram FORK, Ang(F) = 3x+20 and Ang(K) = 7x. What is the measure of Ang(F)?
200 points to the other team who can convert the answer to radians
68 degrees
FULLY describe the transformation on Slide 118.
This is a Rotation
About point P (Center)
that goes counterclockwise (Direction)
90 degrees (Angle of Rotation)
Given the P(2, -3) and Q(-5, 4), find the length of PQ rounded to the nearest tenth.
9.9 units
Can we conclude that these triangles are congruent? Why or why not? (Slide 111)
Yes, because the vertical angles (Ang(JGH) and Ang(MGK)) are congruent so we have ASA congruence.
What is standard form version of this circle's equation: y2 + 4x - 20 - 2y = -x2?
Given quadrilateral BRUH, what tool could I use to prove that BRUH is a rhombus and why?
150 points to the other team that can figure out the alternative strategy
Use distance formula to prove all sides are congruent
Use slope to prove diagonals are perpendicular
Describe the composition of transformations that maps Tri(ABC) onto Tri(A''B''C''). (Slide 119)
1) Translate Tri(ABC) 4 units down, 5 units right
2) Reflect Tri(A'B'C') over the x-axis (y=0)