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Students use this applet to investigate the properties of a rhombus.

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Questions: 1) Is a rhombus a parallelogram? Explain why or why not. 2) Are opposite sides of a rhombus congruent? 3) Are opposite angles of a rhombus congruent? 4) Do the diagonals of a rhombus bisect each other? 5) Does a diagonal of a rhombus bisect a pair of opposite angles? 6) Are the diagonals of a rhombus perpendicular? 7) Are the diagonals of a rhombus congruent? 8) Does either diagonal of a rhombus serve as a line of symmetry? If so, how many?

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Questions: 1) Is a rhombus a parallelogram? Explain why or why not. 2) Are opposite sides of a rhombus congruent? 3) Are opposite angles of a rhombus congruent? 4) Do the diagonals of a rhombus bisect each other? 5) Does a diagonal of a rhombus bisect a pair of opposite angles?

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Area of Rhombus using Diagonals Investigation

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Use the applet to discover the properties of the Rhombus. Move point A to change the size and shape of the Rhombus.

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What are the characteristics of rhombuses?

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Explore characteristics of rhombuses using the ruler and folding up. 中文版：[url]18975 菱形有甚麼特性？[/url] Anthony Or Education Bureau, Hong Kong

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BE SURE to move the vertices and sides of this rhombus around after completing each step in order to help you make more informed conjectures: 1) Measure and display the lengths of all 4 sides. What, if anything, do you notice? Describe in detail. 2) Construct the midpoint of segment AC (even though you haven't constructed segment AC yet.) Label this point "E". 3) Construct segments with lengths AE, BE, CE, & DE. Then measure and display their lengths. What do you notice? Describe in detail. 4) Measure & display the measures of the following angles: Angle BAE, EAD, ADE, EDC, DCE, ECB, CBE, EBA. What do you notice? Describe in detail. 5) Measure display just one of the four angles you see with vertex E. 6) Construct polygon (triangle) ABC. Then reflect this polygon about diagonal AC. 7) Use GeoGebra to "UNDO" step (6) and step (5). Now construct polygon (triangle) DBA. Then reflect this polygon about diagonal DB. Questions to answer/consider: 1) Are opposite sides of a rhombus congruent? 2) Are opposite angles (ENTIRE ANGLES-like angle DAB & angle DCB) of a rhombus congruent? 3) Do the diagonals of a rhombus bisect EACH OTHER? 4) Does a diagonal of an rhombus bisect a pair of opposite angles? If so, how many diagonals do this? 5) Are the diagonals of a rhombus perpendicular? 6) Are the diagonals of a rhombus congruent? 7) Does either diagonal of a rhombus serve as a line of symmetry? If so, how many? 8) **Is a rhombus a parallelogram? If so, WHY is it a parallelogram? 9) What properties are UNIQUE to a rhombus? That is, what properties ALWAYS hold true for a RHOMBUS but do NOT always hold true, in general, for a parallelogram?

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BE SURE to move the vertices and sides of this rhombus around after completing each step in order to help you make more informed conjectures: 1) Measure and display the lengths of all 4 sides. What, if anything, do you notice? Describe in detail.

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Students: The applet below contains a quadrilateral thatALWAYS remains a rhombus. Be sure to move the BIG WHITE VERTICES of this rhombus around as you answer each investigation question!Teachers: A PDF copy of this investigation & its questions can be found below the applet.

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Rhombus Template with Investigation Questions

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Students: The applet below contains a quadrilateral thatALWAYS remains a rhombus. Be sure to move the BIG WHITE VERTICES of this rhombus around as you answer each investigation question!Teachers: A PDF copy of this investigation & its questions can be found below the applet.

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Rhombus Properties illustrated here without any segment lengths or angle measures

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Area of a Rhombus: Quick Modifiable Interactive Discovery

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Investigate the properties of a rhombus using a dynamic sketch.

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An exploration of properties of a rhombus.

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change the shape and orientation of the rhombus

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change the shape and orientation of the rhombus

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Investigating the properties of a rhombus