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“Euclidean Geometry” – UNIT II: Polygons/Circles
High School Mathematics
“Geometry” published by HOLT, RINEHART, & WINSTON
Target Time: 25-27 days
ESSENTIAL STANDARD
ESSENTIAL
QUESTION
DEPTH for
MASTERY
Sections
#2—Uses algebraic skills and concepts to solve
geometric problems throughout geometry
What algebra skills and
concepts are utilized in
geometry?
All
Throughout
unit
#11—Classifies triangles as acute, right, obtuse,
equilateral, isosceles, scalene; and classifies
polygons as regular, convex, congruent
What are the basic
classifications of triangles
and polygons?
All
3.1
3.6
#14—States and applies the triangle sum,
exterior angles, and polygon angle sum theorems
How do you find the sum of
the interior and exterior
angles of any polygon?
All
3.5
3.6
#19—States and applies properties of triangles
and quadrilaterals such as parallelograms,
rectangles, rhombi, squares, and trapezoids
What are the properties of
triangles and quadrilaterals
and how are they used?
All
3.2
4.5
4.6
#21—Uses properties of quadrilaterals to
establish and test relationships involving
diagonals, angles, and lines of symmetry
How do you use properties
of quadrilaterals to
establish relationships
among diagonals, angles, and
lines of symmetry?
All
4.5
4.6
#26—States and applies the Pythagorean
Theorem and its converse
What are the applications
of the Pythagorean
Theorem and its converse?
All
5.4
5.5
5.6
5.7
#27—States and applies properties of special
right triangles, such as 45-45-90 and 30-60-90
triangles
What are the properties of
special right triangles and
how are they used?
All
5.5
COMMENTS
Introduce area and perimeter
Teach midsegment of trapezoid and
median of trapezoid as synonymous
terminology
ESSENTIAL
QUESTION
DEPTH for
MASTERY
Sections
COMMENTS
How do you solve a right
triangle using trigonometric
functions?
Without calculator
or computer
10.1
10.2
Teach inverse sine and “arcsin” as
synonymous terminology
Save technology for enrichment unit
How is trigonometry used in
real world applications?
Without calculator
or computer
10.1
10.2
Teach inverse sine and “arcsin” as
synonymous terminology
Save technology for enrichment unit
All
9.1
9.2
9.3
9.4
9.5
Introduce area and circumference
How do you apply the
relationships among circles,
lines, segments, and the
angles they form?
All
9.1
9.2
9.3
9.4
9.5
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
#20—Recognizes and applies the properties of
inequalities to the measures of segments and
angles in triangles
How are inequalities related
to segments and angles in
triangles?
All
5.4
4.8
ESSENTIAL STANDARD
#28—Identifies and evaluates tangent, sine, and
cosine ratios for an acute angle of a right
triangle; uses a table, calculator, or computer to
find the ratio for a given angle or find the angle
for a given ratio
#29—Uses the tangent, sine, and cosine ratios
for right triangles to solve application problems
such as indirect-measurement problems
#30—Identifies and defines circles and their
parts (center, arc, interior, exterior); segments
and lines associated with circles (chord, diameter,
radius, tangent, secant); properties of circles
(congruent, concentric, tangent); relationship of
polygons and circles (inscribed, circumscribed);
angles (central; inscribed; formed by tangents,
chords, and secants)
#31—Applies geometric relationships to solving
problems, such as relationships between lines and
segments associated with circles, the angles they
form, and the arcs they subtend; and the
measures of these arcs, angles, and segments
What are the parts of a
circle and how are they
related to other geometric
figures?
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
#48—Uses coordinate methods to explore, make
conjectures, or prove properties of geometric
figures, using tools such as 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
Throughout
unit
How can coordinate
methods be used to explore
geometry?
All
Supplement
EOCT Domains Taught in this Unit: Polygons and Circles; Coordinate Geometry
COMMENTS