CK12 - Geometry

Prove:

Statement Reason

1. 
   
   
   
   1. Given
   
   
   2. Given
   
   
   
   


2. 
   


3. 
   
   
   
   3. AlternateInteriorAnglesTheorem
   
   
   
   


4. Add auxiliaryline 4. Line Postulate


5. 
   
   
   
   5. ReflexiveProperty
   
   
   6. SAS TriangleCongruencePostulate
   
   
   
   


6. 
   


7. 
   
   
   
   7. Definitionof congruenttriangles
   
   
   8. Converse of Alternate Interior Angles
   
   
   
   


8. Theorem


9. If the congruentsidesare not the parallelsides,then you can makeeithera parallelogram(in black)or
   an isoscelestrapezoid(in red):

Rhombi,Rectangles,and Squares

LearningObjectives

• Identifythe relationshipbetweenthe diagonalsin a rectangle.


• Identifythe relationshipbetweendiagonalsin a rhombus.


• Identifythe relationshipbetweendiagonalsand oppositeanglesin a rhombus.


• Identifyand explainbiconditionalstatements.

Introduction

Nowthat you havea muchbetterunderstandingof parallelograms,you can beginto look morecarefully
into certaintypesof parallelograms.This lessonexplorestwo very importanttypesof parallelograms—rect-
anglesand rhombi.Rememberthat all of the rulesthat applyto parallelogramsstill applyto rectanglesand