Quadrilaterals
Standards, Targets & Sub-Targets
Practice 1. Make sense of problems and persevere in solving them.
Practice 3 Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics. Practice 5. Use appropriate tools strategically. Practice 6. Attend to precision.
 Major Content
 Supporting Content  Additional Content
 Major Content
BIG IDEA: Use evidence to prove quadrilaterals geometrically and algebraically.
G-COc I can prove geometric theorems.
 Use triangle congruence to prove theorems about
CONGRUENCE (CO)
parallelograms
 Prove geometric theorems
 Know definition of parallelogram
G.CO.11 Prove theorems about parallelograms. Theorems include:
 Know how to create a proof using either flow chart or 2
opposite sides are congruent, opposite angles are congruent, the
column proof structure
diagonals of a parallelogram bisect each other, and conversely,
 Given a parallelogram, prove the characteristics of the
rectangles are parallelograms with congruent diagonals.
parallelogram ex. Opp angles are congruent, opp sides are
congruent, diagonals bisect each other.
 Given a quadrilateral, prove that it is a parallelogram
 Know which quadrilaterals are parallelograms and be able
to prove, ex. Rectangle, square, rhombus
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol ().
Quadrilaterals
Standards, Targets & Sub-Targets
Practice 1. Make sense of problems and persevere in solving them.
Practice 3 Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics. Practice 5. Use appropriate tools strategically. Practice 6. Attend to precision.
 Major Content
 Supporting Content  Additional Content
 Know all of the properties of parallelogram; opp sides are
congruent, opp angles are congruent, diagonals bisect each
other
 Use slope formula to prove sides are parallel
 Use distance formula to prove sides are congruent
 Use distance formula and midpoint to show that diagonals
bisect each other
 Know the properties of a rectangle; all 4 angles are 90
degrees (use slope formula to prove perpendicular),
diagonals are congruent (use distance formula to prove)
 Know the properties of a square; sides are congruent
(distance), angles are 90 (slope), diagonals are
perpendicular (use slope formula to show perpendicular)
 Know properties of rhombus; all sides congruent (distance
formula), diagonals are perpendicular (slope), can show that
sides are not perpendicular (slope)
 Given a circle and the radius prove or disprove if a given
point lies on the circle (Pythagorean theorem)
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EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS (GPE)
 Use coordinates to prove simple geometric theorems
algebraically
G.GPE.4 Use coordinates to prove simple geometric theorems
algebraically. For example, prove or disprove that a figure defined
by four given points in the coordinate plane is a rectangle; prove or
disprove that the point (1, √3) lies on the circle centered at the
origin and containing the point(0, 2).
G-COd I can make geometric constructions.
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol ().
Quadrilaterals
Standards, Targets & Sub-Targets
Practice 1. Make sense of problems and persevere in solving them.
Practice 3 Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics. Practice 5. Use appropriate tools strategically. Practice 6. Attend to precision.
 Major Content
 Supporting Content  Additional Content
 Understand that the compass preserves distance
 Understand that the method for constructing an equilateral
triangle is also a form of constructing a 60 degree angle
 Know how to construct perpendicular segments
 Be able to construct a square given only a perpendicular
and a length
 Understand that a hexagon is composed of equilateral
triangles.
 The radius of a circle is the same as the side length of a
hexagon. Select a point on the circle and mark off the
radius length six times as you go around the circle. The
intersections of the arcs and the circle are the vertices of the
hexagon.
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 Make geometric constructions
G-CO.13 Construct an equilateral triangle, a square, and a regular
hexagon inscribed in a circle. [Focus on construction of an
equilateral triangle.]
G-C I understand and can apply theorems about circles.
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol ().
Quadrilaterals
Standards, Targets & Sub-Targets
Practice 1. Make sense of problems and persevere in solving them.
Practice 3 Construct viable arguments and critique the reasoning of others.
Practice 4. Model with mathematics. Practice 5. Use appropriate tools strategically. Practice 6. Attend to precision.
 Major Content
 Supporting Content  Additional Content
Circles (G-C)
 Understand and apply theorems about circles.
G-C.3 Construct the inscribed and circumscribed circles of a
triangle, and prove properties of angles for a quadrilateral inscribed
in a circle. [Focus on inscribed and circumscribed circles of a
triangle.]
 Define the terms inscribed, circumscribed, angle bisector
and perpendicular bisector
 Know how to construct angle bisectors
 The intersection of angle bisectors is the incenter
 The incenter is the center of the circle inscribed in a triangle
 The incenter is an equal distance from each side of the
triangle
 Know how to construct perpendicular bisectors
 The intersection of perpendicular bisectors is the
circumcenter
 The circumcenter is the center of the circumscribed circle
of the triangle
 The circumcenter is an equal distance from the vertices of
the triangle
 Prove that opposite angles of a quadrilateral inscribed in a
circle are supplementary
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol ().