MATHEMATICS DEPARTMENT CURRICULUM
Syllabus – Geometry
INSTRUCTOR: Kenneth R. Valiska
SCHOOL YEAR: 2015-2016 PERIOD: 4th (10:15-11:10) COURSE NUMBER: 317
COURSE DESCRIPTION
This is the second course in the college preparatory mathematics sequence. Units of study include the fundamentals of Geometry, logic and proof,
parallel and perpendicular lines, triangles, polygons, ratio, proportion and similarity, right triangle trigonometry, area, surface area and volume,
circles and transformations. Technological tools, such as the TI graphing calculator, Geometers Sketchpad and Cabri Junior, will be used for both
discovery and problem solving. Classroom sets of graphing calculators will be provided. Students will be expected to bring a TI-30X IIS scientific
calculator to class on a daily basis.
ENDURING UNDERSTANDINGS - After successfully completing this course, the student will understand that:
1.
2.
3.
4.
5.
Points, lines and planes are the essential building blocks for creating the shapes and dimensions of our world.
Proportions and ratios, including trigonometric ratios, are used to create maps, artwork, architecture and many other things in the real world.
Polygons and circles are the fundamental building blocks for the aesthetic and structural world around us.
In order to form logical arguments, complex ideas are developed through the connection of smaller, previously accepted or proven ideas.
Measurement is used to describe and analyze the sizes, area and capacities of many things in our world.
CREDIT:
1 credit
LEVEL:
10 – Regular
PREREQUISITES
This course is open to sophomores, juniors and seniors who have passed both semesters of Algebra 1
AREAS OF STUDY
First Semester
1 Tools of Geometry
2 Reasoning and Proof
3 Parallel and Perpendicular Lines
4 Congruent Triangles
5 Relationships Within Triangles
8 Similarity
Second Semester
9 Right Triangle Trigonometry
6 Quadrilaterals
7 Area
10 Surface Area and Volume
11 Circles
12 Transformations
II. Prentice
Unit IIHall
– Parallel and Perpendicular
Lines
EngageNY.org
Students
will
be
able
to
use
slope
formula
to:
Geometry book
i.
determine if lines are parallel
I.
Unit 1 – Foundations of Geometry
ii.
if lines are perpendicular
a.
Students will be able to define the following:
1-2 &determine
1-3
iii.
determine
if lines intersectGEO-M3L5
i.
points / collinear / non-collinear
b.
Students will be able to construct:
ii.
lines
i.
parallel lines (translations)
iii.
rays
aa.
two parallel lines
iv.
segments
bb.
more than two parallel lines
v.
angles
ii.
perpendicular lines (rotation)
vi.
etc
iii.
b.
Students will be able to construct
1-5 perpendicular bisectors
c.
Students will be able to apply the relationships between angles whe
i.
circle (talk about radii and congruency here)
lines
intersect:
ii.
line segments
i.
vertical angles
iii.
angles
ii.
linear pair
iv.
congruent segments – introduce transformations here!!
d.
Students
will be able to classify angle relationships formed by paralle
v.
congruent angles – continue talking about transformations here!!
cutand
by a transversal:
c.
Students will be able to measure segments and angles using a protractor
1-4 & p. 708
i.
alternate interior
ruler.
ii.
alternate exterior
d.
Students will be able to classify angles
G7-M6L1 to L3
iii.
corresponding
angle
i.
acute, obtuse, right, straight
1-4
iv. 2-5 same-side interior
ii.
complementary, supplementary, adjacent
v. 1-5 same-side exterior
e.
Students will be able to construct angle bisectors
e.
Students will be able to apply the relationship between parallel lines a
f.
Students will be able to apply the following formulas:
measurements
i.
midpoint formula in the coordinate plane
1-6 of the angle pairs formed
f.
Students
will be able to use angle relationships to explain if lines are
ii.
midpoint formula on a line segment
Semester One
a.
aa.
construct with straightedge and compass (manipulative or
III.
digital) the midpoint of a given line segment
a.
iii.
Pythagorean theorem
aa.
for finding side lengths of right triangle
bb.
on the coordinate plane (distance formula – no triangles)
g.
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
b.
iv.
circles (circumference)
1-5
Unit III – Triangles!!!
Students will be able to identify G8-M2L15
and classify:to L16
i. 7-2 by sides
given three sides
1-6 aa.
bb.
using distance formula
1-7
G6-M5L1 to L4, L6
ii.
by angles
aa.
given three angles
bb.
slope
cc.
converse of Pythagorean Theorem
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 use to classify polygons by:
i.
number of sides
ii.
concave vs. convex
iii.
regular vs. non-regular
e.
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
f.
Students will be able to perform transformations on triangles to show
congruency using:
i.
translations
ii.
reflections
iii.
rotations
g.
Students will be able to explain the triangle congruence postulates/theorems:
i.
sss
ii.
sas
iii.
asa
iv.
aas
vi.
HL
h.
Students will be able to define and construct in all types of triangles:
i.
medians (midpoint formula)
ii.
altitudes (slope)
iii.
angle bisectors
i.
Students will be able to make connections about the correspondence of the
remaining pieces of congruent triangles
j.
Students will be able to dilate a triangle in the coordinate plane
k.
Students will be able to determine the scale factor of dilated triangles using:
i.
side lengths
ii.
distance formula
l.
Students will be able to determine if triangles are similar using a scale factor
m.
Students will be able to find missing sides of similar triangles using the scale
factor
3-3
3-4
G8-M1L8
3-4
G8-M2L13, L14
NA
GEO-M1L12 to 16, G8M2L1, L4 to L6
4-1, 4-2, 4-3, 4-6
G7-M6L5, L14 GEOM1L22, L24 to L27
5-3
GEO-M1L29, L30
GEO-M1L3
4-1 & 4-4
12-7
8-4
G8-M3L1
GEO-M2L2
8-3
8-2
GEO-M2L5, L15, L17
GEO-M2L16, L20, L49
Students will be able to find the surface area of:
i.
prisms
ii.
cylinders
I.
Foundations for Semester Two
a.
Students will be able to identify the base for three-dimensional figures
iii. 10-3pyramids
b.
Students will be able to transform polygons:
iv.
cones
i.
in a plane
v. 12-1,
spheres
12-2, 12-3
ii.
in the coordinate plane
c.
Students
12-1, will
12-2,be12-3
able to find the volume of:
iii.
via dilations
i. 12-7prisms
c.
Students will be able to understand radicals:
ii. p. 355
cylinders
& p. 717
GEO-M2L22, L23
i.
simplify
iii.
pyramids
ii.
rationalization
iv.
cones
iii.
multiplication
v.
spheres
iv.
division
vi.
oblique figures
vii.
estimation of real life figure by relating them to geometric figu
II.
Right Triangles and Trigonometry
a.
Students will be able to construct both:
NA
GEO-M2L24
IV.
Circles
i.
30-60-90 triangles using equilateral triangles
a.
Students will be able to relate central angles and arcs
ii.
45-45-90 triangles using squares
i.
measure
b.
Students will be able to find sides of special right triangles given only one side:ii. 7-3 length
i.
30-60-90 triangles
b.
Students will be able to find the area of a sector
ii.
45-45-90 triangles
c.
Students will be able to relate inscribed angles and arcs
c.
Students will be able understand and apply to the three basic trigonometric
d.
Students
9-1 &will
9-2 be able to construct:G-M2L25, L26, L28
ratios (sin, cos, tan) to:
i.
inscribed circle (perpendicular bisectors)
i.
find missing side
ii.
circumscribed circles (angle bisectors)
ii.
find missing angle
d.
Students will be able to use properties
GEO-M2L34
of opposite angles of an inscribe
iii.
angles of elevation and depression
quadrilateral
9-3
GEO-M2L34
iv.
solving right triangles
e.
Students will be able to apply chord, tangent, secant, and radius proper
d.
Students will be able to find the area triangles when a height or base length is i. 7-4 radius-chord intersections
missing
ii.
radius-tangent intersections
iii.
chord-chord intersections
III.
Area, Surface Area, and Volume
a.
Students will be able to find the area of (based on breaking figure into
iv.
secant-secant intersectionsG6-M5L5, L8, L9 G7triangles):
v.
secant-tangent intersections
M3L19, 20
i.
parallelogram
g.
Students
7-1 will be able understand equations
GEO-M1L28
of circles:
ii.
trapezoid
i. 7-4 identify center and radius, given
GEO-M4L9,
an equation
L10 in standard form
iii.
kite
ii. 7-4 graph given the equation in standard form
iv.
rhombus
iii. 7-4 write the standard equation of a circle given a circle in the coor
v.
regular polygon
plane
7-5
aa.
equilateral triangle
iv.
determine if a given point is on the circle given the standard eq
bb.
hexagon
cc.
n-gon (differentiated by the teacher)
Semester Two
b.
V.
a.
Proofs
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
Ch 4