Download Syllabus for Geometry

Semester One
I.
Unit 1 – Foundations of Geometry
a.
b.
c.
d.
e.
f.
II.
Students will be able to define the following:
i.
points / collinear / non-collinear
ii.
lines
iii.
rays
iv.
segments
v.
angles
vi.
etc
Students will be able to construct
i.
circle (talk about radii and congruency here)
ii.
line segments
iii.
angles
iv.
congruent segments – introduce transformations here!!
v.
congruent angles – continue talking about transformations here!!
Students will be able to measure segments and angles using a protractor
and ruler.
Students will be able to classify angles
i.
acute, obtuse, right, straight
ii.
complementary, supplementary, adjacent
Students will be able to construct angle bisectors
Students will be able to apply the following formulas:
i.
midpoint formula in the coordinate plane
ii.
midpoint formula on a line segment
aa.
construct with straightedge and compass (manipulative or
digital) the midpoint of a given line segment
iii.
Pythagorean theorem
aa.
for finding side lengths of right triangle
bb.
on the coordinate plane (distance formula – no triangles)
Unit II – Parallel and Perpendicular Lines
a.
Students will be able to use slope formula to:
i.
determine if lines are parallel
ii.
determine if lines are perpendicular
iii.
determine if lines intersect
b.
Students will be able to construct:
i.
parallel lines (translations)
aa.
two parallel lines
bb.
more than two parallel lines
ii.
perpendicular lines (rotation)
iii.
perpendicular bisectors
c.
Students will be able to apply the relationships between angles when
two lines intersect:
i.
vertical angles
ii.
linear pair
d.
e.
f.
III.
Students will be able to classify angle relationships formed by parallel
lines cut by a transversal:
i.
alternate interior
ii.
alternate exterior
iii.
corresponding angle
iv.
same-side interior
v.
same-side exterior
Students will be able to apply the relationship between parallel lines and
the measurements of the angle pairs formed
Students will be able to use angle relationships to explain if lines are
parallel
Unit III – Triangles!!!
a.
Students will be able to identify and classify:
i.
by sides
aa.
given three sides
bb.
using distance formula
ii.
by angles
aa.
given three angles
bb.
slope
cc.
converse of Pythagorean Theorem
b.
Students will be able to define and construct:
i.
equilateral
ii.
isosceles
c.
Students will be able to apply the triangle angle sum theorem to:
i.
find the measure of interior angle measures
ii.
find the measure of exterior angles
d.
Students will be able to perform transformations on triangles to show
congruency using:
i.
translations
ii.
reflections
iii.
rotations
e.
Students will be able to explain the triangle congruence
postulates/theorems:
i.
sss
ii.
sas
iii.
asa
iv.
aas
vi.
HL
f.
Students will be able to define and construct in all types of triangles:
i.
medians (midpoint formula)
ii.
altitudes (slope)
iii.
angle bisectors
g.
Students will be able to make connections about the correspondence of the
remaining pieces of congruent triangles
h.
Students will be able to dilate a triangle in the coordinate plane
i.
j.
k.
Students will be able to determine the scale factor of dilated triangles
using:
i.
side lengths
ii.
distance formula
Students will be able to determine if triangles are similar using a scale
factor
Students will be able to find missing sides of similar triangles using the
scale factor
Semester Two
I.
Foundations for Semester Two
a.
Students will be able to understand the concept of area and perimeter for
the following figures
i.
triangles (very basic – given base and height)
ii.
rectangles
iii.
squares
iv.
circles (circumference)
b.
Students will be use to classify polygons by:
i.
number of sides
ii.
concave vs. convex
iii.
regular vs. non-regular
c.
Students will be able to find for polygons:
i.
total angle sum
ii.
total exterior angle sum
iii.
measure of one interior angle
iv.
measure of one exterior angle
d.
Students will be able to identify the base for three-dimensional figures
e.
Students will be able to transform polygons:
i.
in a plane
ii.
in the coordinate plane
iii.
via dilations
f.
Students will be able to understand radicals:
i.
simplify
ii.
rationalization
iii.
multiplication
iv.
division
II.
Right Triangles and Trigonometry
a.
Students will be able to construct both:
i.
30-60-90 triangles using equilateral triangles
ii.
45-45-90 triangles using squares
b.
Students will be able to find sides of special right triangles given only one
side:
i.
30-60-90 triangles
ii.
45-45-90 triangles
c.
Students will be able understand and apply to the three basic trigonometric
ratios (sin, cos, tan) to:
III.
IV.
i.
find missing side
ii.
find missing angle
iii.
angles of elevation and depression
iv.
solving right triangles
d.
Students will be able to find the area triangles when a height or base
length is missing
Area, Surface Area, and Volume
a.
Students will be able to find the area of (based on breaking figure into
triangles):
i.
parallelogram
ii.
trapezoid
iii.
kite
iv.
rhombus
v.
regular polygon
aa.
equilateral triangle
bb.
hexagon
cc.
n-gon (differentiated by the teacher)
b.
Students will be able to find the surface area of:
i.
prisms
ii.
cylinders
iii.
pyramids
iv.
cones
v.
spheres
c.
Students will be able to find the volume of:
i.
prisms
ii.
cylinders
iii.
pyramids
iv.
cones
v.
spheres
vi.
oblique figures
vii.
estimation of real life figure by relating them to geometric figures
Circles
a.
Students will be able to relate central angles and arcs
i.
measure
ii.
length
b.
Students will be able to find the area of a sector
c.
Students will be able to relate inscribed angles and arcs
d.
Students will be able to construct:
i.
inscribed circle (perpendicular bisectors)
ii.
circumscribed circles (angle bisectors)
e.
Students will be able to use properties of opposite angles of an inscribed
quadrilateral
f.
Students will be able to apply chord, tangent, secant, and radius properties:
i.
radius-chord intersections
ii.
radius-tangent intersections
iii.
chord-chord intersections
g.
V.
iv.
secant-secant intersections
v.
secant-tangent intersections
Students will be able understand equations of circles:
i.
identify center and radius given an equation in standard form
ii.
graph given the equation in standard form
iii.
write the standard equation of a circle given a circle in the
coordinate plane
iv.
determine if a given point is on the circle given the standard
equation
Proofs
a.
Students will be able to prove conjectures about triangles using
i.
sss
ii.
sas
iii.
asa
iv.
aas
v.
HL
vi.
CPCTC (differentiated by the teacher)
aaa. proving lines parallel
bbb. proving second sets of triangles congruent
ccc. proving properties of quadrilaterals