Arcs and Triangles

Given isosceles triangle ABC whose length of the shorter leg is n, and arcs center at B and C, what is the area of the shaded part?

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Download File

Two Squares and a Quadrilateral

A common vertex is shared by two squares A. Quadrilateral HIJK is formed using the segments joining the vertices and the midpoints of the diagonals of the square. What is the shape of the quadrilateral?

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Questions

1. Move the vertices of the two squares. Are your observations still the same? 
2. Make a conjecture about your observation. 
3. Prove your conjecture. 

Download File

Reference
 http://www.ies.co.jp/math/java/geo/twosqsq/twosqsq.html

Segment Division

This applet shows how to divide a segment into n equal parts. A slider was used together with the segment command. This is the output of GeoGebra Tutorial 16 - Slider, Sequence, and Segment Division of the GeoGebra Intermediate Tutorial Series.  This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Download File

Folded Tape

Drag the blue point to fold the tape. What type of triangle is the overlapped part? Justify your answer.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Download File