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“Honors Euclidean Geometry” – UNIT I: Logic and Reasoning, Points/Lines/Planes/Angles
“Geometry” published by HOLT, RINEHART, & WINSTON
Target Time: 13-17 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
1.1
1.2
1.3
1.4
#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)
What properties are
associated with points,
segments, angles, lines, and
planes?
All
How are lines, planes, and
angles related?
All
#45—Applies the distance and midpoint formulas
How are the distance and
midpoint formulas used?
All
5.6
IMPORTANT STANDARD
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
How do we solve problems
and practical applications
and judge the
reasonableness of the
results?
All
Throughout
unit
#4—Uses inductive and deductive reasoning to
reach conclusions, identifies conjectures and
What is the difference
between inductive and
All
2.1
2.2
3.3
(skew p380)
Parallel and Perpendicular Postulates
COMMENTS
counterexamples, and describes the nature of a
deductive mathematical system
deductive reasoning?
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
#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
How can visualization skills
help you explore both solid
and plane geometry?
Lines, points,
planes, two- and
three- dimensional
1.1
What are the basic tools
and construction methods
used in geometry?
OMIT proportional
segments;
tangents; and
inscribed and
circumscribed
polygons
Throughout
unit
All
Supplement
All
Supplement
All
Supplement
#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
#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
#44—Identifies and graphs ordered pairs of
numbers in the coordinate plane
#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
How do we graph and/or
identify ordered pairs in a
coordinate plane?
How do we find the slope,
equation, and graph of a
line?
How do you find the
coordinates of the point of
intersection of two lines in
the coordinate plane?
Deemphasize formal proof and
emphasize logic
COMMENTS
EOCT Domains Taught in this Unit: Logic and Reasoning; Points, Lines, Planes, and Angles; Coordinate Geometry