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“Euclidean Geometry” – UNIT I: Logic and Reasoning, Points/Lines/Planes/Angles
High School Mathematics
“Geometry” published by HOLT, RINEHART, & WINSTON
Target Time: 15-17 days
ESSENTIAL STANDARD
ESSENTIAL
QUESTION
DEPTH for
MASTERY
Sections
COMMENTS
#2—Uses algebraic skills and concepts to solve
geometric problems throughout geometry
What algebra skills and
concepts are utilized in
geometry?
All
Throughout
unit
Stress algebra
#5—Recognizes valid deductive reasoning;
constructs and uses if-then, converse, inverse,
and contrapositive statements.
What are the different forms
of a conditional statement?
All
2.2
12.3
#8—Identifies, describes, and contrasts
points, lines, planes, segments, and rays
What are the characteristics
of points, lines, planes,
segments, and rays?
All
1.1
How are segments and angles
measured and classified?
All
1.2
1.3
What properties are
associated with points,
segments, angles, lines, and
planes?
All
1.1
1.2
1.3
1.4
How are lines, planes, and
angles related?
All
How are the distance and
midpoint formulas used?
All
#9—Identifies, defines, estimates, and
measures segments and angles (acute, obtuse,
right, straight, complementary, supplementary,
adjacent, vertical, congruent, and linear pair)
#10—Identifies and defines or describes
properties associated with points (distance,
between, collinear, coplanar), segments
(midpoint, congruence, interior, exterior), and
lines and planes (perpendicular, parallel,
intersecting)
#12—Recognizes parallel lines and planes, skew
lines, and pairs of angles formed when two lines
are cut by a transversal (alternate and same
side, interior and exterior, corresponding)
#45—Applies the distance and midpoint
formulas
3.3
(skew p380)
5.6
Parallel and Perpendicular Postulates
ESSENTIAL
QUESTION
DEPTH for
MASTERY
Sections
#1—Solves problems and practical applications
using appropriate approaches and tools
(including calculators and computers) and
judges the reasonableness of results
#4—Uses inductive and deductive reasoning to
reach conclusions, identifies conjectures and
counterexamples, and describes the nature of a
deductive mathematical system
How do we solve problems and
practical applications and
judge the reasonableness of
the results?
All
Throughout
unit
What is the difference
between inductive and
deductive reasoning?
All
2.1
2.2
2.5
#6—Uses formal and/or informal logical
reasoning processes
How do you use formal and
informal reasoning processes?
All
2.1
2.2
2.5
#7—Uses inductive and deductive reasoning to
prove conjectures in written form such as
paragraph, two-column, or flow chart
How do your prove theorems
and how do you demonstrate
conjectures?
All
2.4
2.5
IMPORTANT STANDARD
#13—Applies basic facts about points, lines,
and planes, and about perpendicular and parallel
lines and planes.
How are points, lines and
planes related?
All
1.1
1.2
1.4
3.3
3.8
COMPACT STANDARD
ESSENTIAL
QUESTION
DEPTH for
MASTERY
Sections
#3—Uses visualization skills to explore and
interpret both two- and three- dimensional
geometric figures using such topics as
projections, cross sections, and locus problems
How can visualization skills
help you explore both solid
and plane geometry?
Lines, points,
planes, two- and
three- dimensional
1.1
COMMENTS
Deemphasize formal proof and
emphasize logic
COMMENTS
COMPACT STANDARD
#16—Uses tools such as compass and
straightedge, paper folding, tracing paper,
mira, or computer to construct congruent
segments, angles, triangles, and circles; an
angle bisector; a perpendicular bisector; a
perpendicular line from a point on a line; parallel
lines; proportional segments; tangents; and
inscribed and circumscribed polygons
#46—Finds the slope of a line, writes an
equation of a line, and graphs equations of lines
#47—Finds the coordinates of the point of
intersection of two lines, using algebra,
graphing, and appropriate technology
ESSENTIAL
QUESTION
DEPTH for
MASTERY
Sections
What are the basic tools and
construction methods used in
geometry?
OMIT proportional
segments;
tangents; and
inscribed and
circumscribed
polygons
Throughout
unit
How do we find the slope,
equation, and graph of a line?
All
Supplement
How do you find the
coordinates of the point of
intersection of two lines in the
coordinate plane?
All
Supplement
COMMENTS
EOCT Domains Taught in this Unit: Logic and Reasoning; Points, Lines, Planes, and Angles; Coordinate Geometry