Symmetry, Transformations, and Segments
Lines, Segments, and Angles
Triangles
Polygons and Quadrilaterals
Logic, Cirlces
100
What type of symmetry does this shape have?
Line symmetry
100
Find x and the length of BC
Part + Part = Whole
AB + BC = AC
9x+7 + -3x+20 = 39
x = 2
BC = 14
100
Given △ABC with m∠A = 45, m∠B = 85, find m∠C.
m∠C = 50
100
What is the sum of the exterior angles of an octagon?
360o.
The sum of the exterior angles for any polygon is 360o.
100
p: I did not bring in a key-lime pie.
q: I passed Geometry class.
Give the original conditional statement in the form:
p-->q
as well as the inverse, converse, and contrapositive.
Conditional: If I did not bring in a key-lime pie, then I passed Geometry class.
Inverse: If I did bring in a key-lime pie, then I did not pass Geometry class.
Converse: If I passed Geometry class, then I did not bring in a key-lime pie.
Contrapositive: If I did not pass Geometry class, then I did bring in a key-lime pie.
200
This image has what type of symmetry?
Point Symmetry
200
Find x and find m∠ABD
The angles are a linear pair:
Part + Part = Whole
5x+10 + 2x-5 = 180
x = 25
m∠ABC = 135
200
Which of the following sets of numbers CAN represent the sides of a triangle?
a) 2,4,8
b) 8,8,5
c) 8,10,2
d) 6,9,15
b) 8,8,5
200
What is the measure of one external angle of a regular 36-gon?
The sum of the exterior angles for any polygon is 360.
360/36 = 10.
One angle measures 10o.
200
Give the meaning of each logic symbol:
~
∧
∨
→
~ "not" (oppostive/inverse)
∧ "and"
∨ "or"
→ "if/then"
300
Find the distance between (3,5) and (9,13).
Distance = 10 units.
300
The point M is the midpoint of segment AB.
Point B has coordinates (-10,6).
Point M has coordinates (-6,8).
What are the coordinates of point A?
A = (-2,10)
300
Which congruence method proves these two triangles are congruent?
SAS
The angles formed at the intersection C are vertical and thus are congruent.
300
What is the sum of the interior angles for a 20-gon?
3240o
You can draw 18 triangles inside a 20-gon and each triangle's angles sum to 180o.
300
Find the radius of a circle whose area is 113.04.
Use the equation A = 𝜋r2.
r = 6
400
What is the slope of the line that passes through the points (5,8) and (-1,-1)?
9/6
OR
3/2
OR
1.5
400
Build and equation and find x.
The angles are congruent.
17x - 4 = 12 + 15x
x = 8
400
Find the lengths of BA and BC
BA: use tangent. BA = 8.40
BC: use cosine. BC = 14.65
400
Given parallelogram ABCD below:
Given AE = 8
Given DB = 12
Find the lengths of:
CE
DE
BE
CE = 8
DE = 6
BE = 6
400
Given circle A below. EB is a diameter.
What is the measure of Arc ED?
Measure of Arc ED = 38o
500
What is the equation of the line of reflection of these figures?
Find the midpoint of A and A': (0.5,-1).
Use the x-value because the line of reflection must be vertical.
x = 0.5
500
Find x, then find the m∠TRQ.
The angles are congruent because they are vertical.
8x = 2x + 72
x = 12
m∠TRQ = 96o
500
Given that the two triangles are similar, find x.
Set up a proportion
13/27 = 21/x
Cross-multiply to create an equation
13x = 27*21
x = 43.6
500
A rectangular park has been built in downtown Richmond. The designer wants to put a gravel walkway diagonally across the park. The width of the park is 80 feet long and the length is 150 feet long. Find the length of the walkway.
The walkway makes the hypotenuse of a right triangle.
The length is 170 feet.
500
Given circle O with an inscribed decagon.
Find:
m∠AOB
and
m∠OCB
Find the measure of an arc made by one side of the decagon: 360o / 10 = 36o. ∠AOB is twice that.
m∠AOB = 72o
m∠OCB = 36o
By the exterior angle theorem, ∠OCB+∠OBC = ∠AOB. The triangle OBC is isosceles since its legs are both radii of the same circle. So, ∠OCB = ∠OBC.