Common Core Geometry. Chapter 6. Quadrilaterals

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So, this is the year when you have to switch over to the new Common Core Standards for high school geometry, but you don't quite know what that means. Or perhaps you know the new standards but haven't had time to re-align your course. I have your answer. I've created a set of PowerPoints and Word worksheets, aligned to the Common Core, that will take you from the first day of the course to the last.

This is Chapter 6 of my Common Core-aligned course in geometry. The topic is angles of polygons and quadrilaterals. Students first draw upon the Triangle Angle Sum Theorem to derive formulae for the sums of the interior and exterior angles of a polygon. After students investigate the various types of quadrilateral - the parallelogram, the rectangle, the rhombus, the square, the kite and the trapezoid. Below are descriptions of the chapters seven sections.

6.1 Angles of Polygons. Students derive the interior angle and exterior angle sum formulae. They are presented with a number of application problems.

6.2 The Parallelogram Proofs. Students prove and then apply the core properties of parallelograms: opposite sides and angles are congruent, consecutive angles are supplementary and diagonals bisect one another.

6.3 The Parallelogram Tests. Students prove and then apply the parallelogram tests. (A quadrilateral is a parallelogram when: opposite sides are congruent, opposite angles are congruent, diagonals bisect one another, one pair of opposite sides are both parallel and congruent.)

6.4 Rectangles. Students prove that rectangles have congruent diagonals and that a parallelogram with congruent diagonals is a rectangle.

6.5 Rhombi and Squares. Students prove the rhombus properties (diagonals are perpendicular, diagonals bisect angles) and the rhombus tests (a parallelogram with perpendicular diagonals is a rhombus, a parallelogram in which diagonals bisect angles is a rhombus).

6.6 Kites. Students prove the kite properties (kites have 1 pair of congruent opposite angles, in a kite 1 diagonal bisects the other, kites have perpendicular diagonals). They also investigate the relation between kites and parallelograms. It is proven that no parallelogram is a kite.

6.7 Trapezoids. Students prove the properties of isosceles trapezoids (diagonals are congruent, same-side base angles are congruent) and the isosceles trapezoid tests (a trapezoid is isosceles when diagonals are congruent and when same-side base angles are congruent). They also investigate the relation of trapezoids to parallelograms and to kites. It is proven that trapezoids are neither kites nor parallelograms.


For each section there is both a PowerPoint and a worksheet. The worksheets give ample practice in the day's topic. Answers are included.

The worksheets are appropriate for both Honors and non-Honors classes. Questions marked H are intended for Honors only. Worksheets include answers to selected questions.

Included is a challenge problem set, appropriate for an Honors-level class. It is intended to be given out on the first day of the chapter and taken up on the last day.

The Preview is is a selection of PowerPoints and worksheets from the chapter.

A description of the course can be found among my downloads. The title is "Course Contents with Commentary".
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2 Weeks

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Common Core Geometry. Chapter 6. Quadrilaterals
Common Core Geometry. Chapter 6. Quadrilaterals
Common Core Geometry. Chapter 6. Quadrilaterals
Common Core Geometry. Chapter 6. Quadrilaterals