FLVS Practice Geometry EOC - Vocabulary & Guided Questions
1)
2)
3)
4)
5)
6)
Transversals
a) Alternate Interior Angles
b) Alternate Exterior Angles
c)
Consecutive (Same Side) Interior Angles
d) Consecutive (Same Side) Exterior Angles
e) Corresponding Angles
f)
Are Alternate Interior/Exterior Angles ALWAYS congruent? When are they not congruent?
g) When are Consecutive (Same Side) Interior/Exterior Angles supplementary?
Triangle Classification
a) Acute
b) Obtuse
c)
Right
d) Scalene
e) Isosceles
f)
Equilateral (Equiangular)
g) Is there such a thing as an Acute Obtuse Triangle? Why or why not?
Coordinate Geometry
a) Midpoint Formula
b) Distance Formula
c)
If you are trying to determine if two segments are congruent (given the endpoints), which
formula do you use?
d) If you are trying to determine where the segment is bisected (given the endpoints), which
formula do you use?
Special Segments in a Triangle & the Points of Concurrency
a) Altitude
b) Perpendicular Bisector
c)
Angle Bisector
d) Median
e) Orthocenter
f)
Circumcenter
g) Incenter
h) Centroid
i)
The Incenter is the center of which circle?
j)
Which point is equidistant from the vertices of the triangle? Why?
k) The special segment going through the Orthocenter makes a ___________ angle with one of
the sides of the triangle.
l)
What is the equation that you can use to find the length of the median of a triangle given the
length from the centroid to the midpoint of the side?
Inequalities in a Triangle/ Hinge Theorem
a) What is true about the side opposite the smallest angle? The largest angle?
b) What does that mean about the hypotenuse in a right triangle?
c)
Hinge Theorem
Triangle Inequalities – What are the possible sides of a triangle
a) If a triangle has sides of lengths 7 & 15. What is the range of possible lengths for the third
side?
7)
8)
9)
Congruent Triangles
a) AAS
b) ASA
c)
SAS
d) SSS
e) What are the two angle-side congruency statements that do not support triangle
congruence?
Similar Polygons
a) Similar
b) Proportion
c)
If a segment is drawn connecting the midpoints of two sides of a triangle, what is the ratio of
the smaller triangle (the one inside) to the larger triangle.
d) If a segment connects two sides of a triangle such that the segment is parallel to the third side
of the triangle, what can you say about the smaller triangle to the larger triangle?
e) If 2 polygons are similar so that one corresponding edge is n times bigger than the other
corresponding edge, what can you say about all the sides of the two polygons?
f)
If 2 polygons are similar so that one corresponding edge is n times bigger than the other
corresponding edge, what can you say about the perimeters of the two polygons? (Hint: What
dimension is perimeter?)
g) If 2 polygons are similar so that one corresponding edge is n times bigger than the other
corresponding edge, what can you say about the areas of the two polygons? (Hint: How many
dimensions is area?)
Right Triangles
a) Special Right Triangles
i)
30⁰-60⁰-90⁰
ii) 45⁰-45⁰-90⁰
iii) Can you make your own short cut? How?
b) Pythagorean Triplets
c)
Geometric Mean
d) Divided Triangle Problems (Two triangles created by drawing the altitude in a triangle)
e) Similar Right Triangles
f)
Pythagorean Theorem & Converse (Is the triangle a right triangle?)
g) Trigonometry & Inverse Trigonometric Ratios
h) Reciprocal Trigonometric Ratios
i)
If two sides of a right triangle are given, what equation do you use to find the third side?
j)
If an angle and a side are given in a right triangle, what type of equation would you use to find
a second side?
k) If you are given two sides of a right triangle, what type of equation would you use to find the
angles?
l)
How many Pythagorean Triplets are there?
m) Could the sides of a 30⁰-60⁰-90⁰ triangle be a Pythagorean Triplet?
10) Special Quadrilaterals
a) Parallelogram
b) Rectangle
c)
Rhombus
d) Square
e) Trapezoid
f)
Isosceles Trapezoid
g) Kite
h) A rhombus MUST also be a ______________?
i)
A rhombus COULD be a _________________?
j)
How is the area of a parallelogram comparable to the area of a rectangle? (Hint: Draw a
parallelogram and then draw the segment from the vertex of the obtuse angle perpendicular
to the opposite side. Repeat with the other obtuse angle. What is the area of rectangle
“inside” the parallelogram? What is the area of the two drawn triangles? How are they
related to the area of the parallelogram?)
k) Which special quadrilaterals MUST have congruent diagonals?
l)
Compare the diagonals of a kite, rhombus, and a parallelogram. For which quadrilaterals are
the diagonals perpendicular? Which condition is shared by those quadrilaterals? Use that
condition to determine whether or not the diagonals are perpendicular in a square and a
rectangle.
m) Use the same type of analysis to determine which condition must be present for the diagonals
to be congruent in a special quadrilateral. Does the isosceles trapezoid fit your condition? If
not expand your condition. (Hint: What about congruent triangles?)
n) Use the same type of analysis to determine which condition must be present for the diagonals
to bisect each other in a special quadrilateral.
o) How are the Mid-Segment Theorem and the area of the trapezoid related?
p) Which special quadrilaterals MUST have congruent opposite sides (both pairs)?
q) Which special quadrilaterals MUST have congruent opposite angles (both pairs)?
r)
How you use the distance formula to verify the classification of a quadrilateral?
s)
How you use the slope formula to verify the classification of a quadrilateral?
t)
How you use the midpoint formula to verify the classification of a quadrilateral?
11) Polygons
a) Convex vs. Concave
b) Sum of the Interior Angles
c)
Sum of the Exterior Angles
d) Interior Angle of a Regular Polygon
e) Exterior Angle of a Regular Polygon
f)
Area of a Regular Polygon
g) Perimeter of a Polygon
h) Number prefixes, i.e. do, tri, quad, tetra, penta, hexa, hepta, octa, nona, deca, undeca,
hendeca, dodeca, trideca (also triskaideca), tetradeca (also tetrakaideca), pentadeca (also
pentakaideca), hexadeca (also hexakaideca), heptadeca, octadeca (also octakaideca),
nonadeca (also enneadecagon or enneakaidecagon), icosa
i)
The formula for the area of a regular n sided polygon in the EOC reference sheet is A= (1/2) Pa
where “P” is perimeter and “a” is the apothem. Show that the formula on the reference sheet
is equivalent to finding the area of the n congruent triangles. Which method do you think is
more useful?
j)
To find the SUM of the exterior angles of a convex polygon, do you need to know the number
of sides?
k) Given the length of a side of a regular n-gon, how do you find the apothem?
l)
Given the length of a side of a regular hexagon, what short cut could you use to find the
apothem?
m) How do you use the apothem to find the area, given the length of a side of a regular polygon?
n) Composite Areas: On the left wall of my room is a poster of The Three Story House. Draw the
house with the three stories. What shapes make up the first two stories? What is the third
story? What shapes make up the chimney? What do you have to measure to find the area of
the house including the chimney?
o) Let’s pretend that we own an ice cream store and we want to make a stylized ice cream cone
out of tile on the front sidewalk. Could you find the area of the ice cream cone by measuring
only two dimensions? What would you measure?
p) Consider the letters of the alphabet written in stylized block capitals. For each letter what
shapes make up the letter? Would you add or subtract the shapes to make the letter?
12) Polyhedra
a) Nets
b) Euler’s Formula
c)
Number of Vertices, Edges, Faces for:
i)
Prisms
ii) Pyramids
iii) Platonic Solids – Tetrahedron
iv) Platonic Solids – Cube
v) Platonic Solids – Octahedron
vi) Platonic Solids – Dodecahedron
vii) Platonic Solids – Icosahedron
13) Surface Area
a) Right Prisms
i)
Cylinder
ii) Rectangular Prisms
iii) Triangular Prisms
iv) Polygonal Prisms
b) Pyramids & Cones
i)
Cone
ii) Triangular Pyramid
iii) Rectangular Pyramid
iv) Polygonal Pyramid
c)
Regular Polyhedra (Platonic Solids)
i)
Tetrahedron
ii) Cube
iii) Octahedron
iv) Dodecahedron
v) Icosahedron
d) Sphere
e) Irregular Polyhedra i.e. cookie jar with conical lid, Jason’s Aquarium, the Washington
Monument, stylized triumphal arch, Dome of the Rock.
f)
Consider the five examples given for Irregular Polyhedra. The cookie jar is #38 in the FLVS
Practice EOC. Jason’s Aquarium is on the Practice EOC given in this class. If you need a picture
of the Washington Monument, a triumphal arch, the Dome of the Rock I will provide one.
What are the faces of each of these irregular polyhedra?
g) If 2 polyhedra are similar so that one corresponding edge is n times bigger than the other
corresponding edge, what can you say about the surface areas of the two polyhedra? (Hint:
How many dimensions is surface area?)
14) Volume
a) Right Prisms
i)
Cylinder
ii) Rectangular
iii) Triangular
iv) Polygonal
b) Oblique Prisms
c)
Pyramids & Cones
i)
Cone
ii) Triangular Pyramid
iii) Rectangular Pyramid
iv) Polygonal Pyramid
d) Regular Polyhedra (Platonic Solids)
i)
Tetrahedron
ii) Cube
iii) Octahedron
iv) Dodecahedron
v) Icosahedron
e) Sphere
f)
Irregular Polyhedra i.e. cookie jar with conical lid, Jason’s Aquarium, the Washington
Monument, stylized triumphal arch, Dome of the Rock.
g)
Consider the five examples given for Irregular Polyhedra. The cookie jar is #38 in the FLVS
Practice EOC. Jason’s Aquarium is on the Practice EOC given in this class. If you need a picture
of the Washington Monument, a triumphal arch, the Dome of the Rock I will provide one.
What are the shapes used to make each of the irregular polyhedra. Would you add or
subtract the shapes?
h) If 2 polyhedra are similar so that one corresponding edge is n times bigger than the other
corresponding edge, what can you say about the volumes of the two polyhedra? (Hint: How
many dimensions is volume?)
15) Circles
a) Circumference
b) Area
c)
Equation of a Circle
i)
Centered at the origin
ii) Centered at (h, k)
d) Arc Measure
e) Arc Length
f)
Area of Sector
g) “Magic Number” Formulas
i)
Arcs and Angles Outside the Circle (i.e. tangents and secants)
ii) Arcs and Angles Inside the Circle (i.e. Intersecting chords)
iii) Central and Inscribed Angles
iv) Angle Formed by Chord Intersecting Tangent
h) Central Angle and Intersecting Tangents
i)
Tangent Intersecting Radius
j)
Draw a circle, two intersecting tangents to the circle and the two radii connecting the tangent
points to the center. What quadrilateral have you drawn? In point of fact, it is a special case
of that kind of quadrilateral. What classification of triangle is formed by the segment
connecting the center of the circle to the intersection of the tangents.
k) What is the difference between Arc Measure and Arc Length?
l)
Compare and contrast Arc Length and Sector Area.
m) Which would you use, Arc Length or Sector Area, to measure how much cloth to use in a quilt
pattern made of circles cut into congruent pieces?
n) Which would you use, Arc Length or Sector Area, to measure how much string to use around
part of a clock?
o) If you were to paint a giant block letter C on the side of a building, what would you need to
measure to find the area?
16) Logic
a) Condition Statements
b) Conditionals (Statements made from a conditional statement).
i)
Converse
ii) Contrapositive
c)
Biconditional Statement
d) Logically Equivalent
e) Supporting Statement
f)
Find the hypothesis and conclusion of : “If , then .”
g) Find the converse of: “If , then .”
h) Negate “".
i)
Find the contrapositive of: “If , then .”