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Geometry Quadrilaterals and Polygons - 18 day full lessons includes lesson plans, worksheets, activities, smart notebook files, ppt, assessments, and answer key

The student will be able to:

Identify the type of quadrilateral represented on a coordinate plane or from given points using slope to determine parallel or perpendicular segments.

Write and solve equations to find missing sides, angles, or other measures of quadrilaterals based on the properties and attributes of the quadrilateral and justify the use of the equation.

Identify parts of a quadrilateral which are congruent, supplementary, parallel, perpendicular, etc. based on the properties and attributes of the given quadrilateral.

Solve real-life application problems involving properties of quadrilaterals.

Use the midsegment of a trapezoid to solve problems.

Connect to midsegment of triangle.

Determine the length of a trapezoid’s midsegment given the lengths of the bases or determine the length of a base given the length of the midsegment and other base.

Use the slope formula to verify the midsegment is parallel to the bases of the trapezoid.

Use midpoint formula to determine the endpoints of the midsegment of a trapezoid.

Use distance formula to verify the relationship between the length of the midsegment and the lengths of the bases of a trapezoid.

Define: parallelogram, rectangle, square, rhombus, trapezoid (including right and isosceles), and kite according to the attributes of each.

Define the midsegment of a trapezoid

Identify a quadrilateral based on a description or diagram.

Distinguish between definitions, postulates, conjectures, and theorems related to quadrilaterals and other polygons.

Write the inverse/converse/contrapositive of a conditional statement about quadrilaterals or other polygons and determine its validity.

Identify the inverse/converse/contrapositive of a conditional statement about quadrilaterals or other polygons from a given set of statements.

Write a biconditional statement about quadrilaterals or other polygons and determine its validity.

Investigate/verify properties of parallelograms regarding opposite sides, opposite angles, consecutive angles, and diagonals.

Compare properties of a rectangle, square, rhombus, trapezoid (including right and isosceles), and kite to those of a parallelogram.

Make and verify conjectures about the angles, sides, diagonals of various quadrilaterals.

- Example: A diagonal drawn in a rectangle forms two congruent triangles.

- Example: because Quad ABCD is a rhombus.

Extend Triangle Sum Theorem to the sum of interior/ exterior angles for other polygons.

Represent the pattern for the measure of one interior angle of a regular polygon of n sides in a variety of ways (algebraically, graphically, etc.).

Use various methods to verify conjectures about quadrilaterals, including

patty paper

coordinate graphing

transformations

Geometer’s Sketchpad or Geometry

compass and straightedge

Classify a quadrilateral as a parallelogram, rectangle, square or rhombus based on the properties of opposite sides, opposite angles or diagonals.

Write a proof of the classification of the quadrilateral using various formats:

Paragraph

Flowchart

Two column

Use various methods to prove theorems

Coordinate

Transformational

Axiomatic

Find missing measurements (angles, sides, etc.) in quadrilaterals and other polygons based on given information and the attributes and properties of the polygons.

Solve problems using properties and attributes of quadrilaterals and other polygons.

The student will be able to:

Identify the type of quadrilateral represented on a coordinate plane or from given points using slope to determine parallel or perpendicular segments.

Write and solve equations to find missing sides, angles, or other measures of quadrilaterals based on the properties and attributes of the quadrilateral and justify the use of the equation.

Identify parts of a quadrilateral which are congruent, supplementary, parallel, perpendicular, etc. based on the properties and attributes of the given quadrilateral.

Solve real-life application problems involving properties of quadrilaterals.

Use the midsegment of a trapezoid to solve problems.

Connect to midsegment of triangle.

Determine the length of a trapezoid’s midsegment given the lengths of the bases or determine the length of a base given the length of the midsegment and other base.

Use the slope formula to verify the midsegment is parallel to the bases of the trapezoid.

Use midpoint formula to determine the endpoints of the midsegment of a trapezoid.

Use distance formula to verify the relationship between the length of the midsegment and the lengths of the bases of a trapezoid.

Define: parallelogram, rectangle, square, rhombus, trapezoid (including right and isosceles), and kite according to the attributes of each.

Define the midsegment of a trapezoid

Identify a quadrilateral based on a description or diagram.

Distinguish between definitions, postulates, conjectures, and theorems related to quadrilaterals and other polygons.

Write the inverse/converse/contrapositive of a conditional statement about quadrilaterals or other polygons and determine its validity.

Identify the inverse/converse/contrapositive of a conditional statement about quadrilaterals or other polygons from a given set of statements.

Write a biconditional statement about quadrilaterals or other polygons and determine its validity.

Investigate/verify properties of parallelograms regarding opposite sides, opposite angles, consecutive angles, and diagonals.

Compare properties of a rectangle, square, rhombus, trapezoid (including right and isosceles), and kite to those of a parallelogram.

Make and verify conjectures about the angles, sides, diagonals of various quadrilaterals.

- Example: A diagonal drawn in a rectangle forms two congruent triangles.

- Example: because Quad ABCD is a rhombus.

Extend Triangle Sum Theorem to the sum of interior/ exterior angles for other polygons.

Represent the pattern for the measure of one interior angle of a regular polygon of n sides in a variety of ways (algebraically, graphically, etc.).

Use various methods to verify conjectures about quadrilaterals, including

patty paper

coordinate graphing

transformations

Geometer’s Sketchpad or Geometry

compass and straightedge

Classify a quadrilateral as a parallelogram, rectangle, square or rhombus based on the properties of opposite sides, opposite angles or diagonals.

Write a proof of the classification of the quadrilateral using various formats:

Paragraph

Flowchart

Two column

Use various methods to prove theorems

Coordinate

Transformational

Axiomatic

Find missing measurements (angles, sides, etc.) in quadrilaterals and other polygons based on given information and the attributes and properties of the polygons.

Solve problems using properties and attributes of quadrilaterals and other polygons.

Total Pages

75 pages

Answer Key

Included

Teaching Duration

3 Weeks

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