Geometry - Prove Quadrilaterals are Parallelograms
Common Core Aligned Lesson with Homework
This lesson includes:
-Lecture Notes (PDF, SMART Notebook, and PowerPoint)
-Blank Lecture Notes (PDF and SMART Notebook)
-Answer Key (PDF)
-Prove that a quadrilateral is a parallelogram.
-Use coordinate geometry with parallelograms.
Common Core Standards:
G.CO.11 - Prove theorems about parallelograms.
G.GPE.4 - Use coordinates to prove simple geometric theorems
Quadrilaterals Lesson Plan Bundle
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© Ashley Spencer, 2014
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The Common Core Standards were written and developed by The National Governors Association Center for Best Practices and Council of Chief State School Officers. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
This product is the work of Ashley Spencer (“Infinitely Pi Learning”). It is intended to support the implementation of the Common Core Standards. Any claim of alignment is the personal opinion of Ashley Spencer (“Infinitely Pi Learning”) and is not necessarily the opinion of the National Governors Association Center for Best Practices and Council of Chief State School Officers. No approval by, nor the association with, the creators of the Common Core Standards is intended or implied.
Lecture - 10, HW - 3
One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel.
There are six important properties of parallelograms to know:
- Opposite sides are congruent (AB = DC).
- Opposite angels are congruent (D = B).
- Consecutive angles are supplementary (A + D = 180°).
- If one angle is right, then all angles are right.
- The diagonals of a parallelogram bisect each other.
- Each diagonal of a parallelogram separates it into two congruent triangles.
$$\triangle ACD\cong \triangle ABC$$
If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi.
If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid. The parallel sides are called bases while the nonparallel sides are called legs. If the legs are congruent we have what is called an isosceles trapezoid.
In an isosceles trapezoid the diagonals are always congruent. The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases.
Find the length of EF in the parallelogram
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