Download Honors Geometry – GSP 4 - Equivalence Instructions

Honors Geometry – GSP 4 - Equivalence
Instructions:
• Complete the following constructions, one per page, in a single sketchpad document.
• Be sure that your figures are correctly labeled, connected and dynamic
• Include an equivalence statement (rectangle ABCD is equivalent to trapezoid CDEF)
• Measure the area of your two figures and display these measurements on your GSP page
• Write a BRIEF explanation, using the correct labels, of the method and connection between the
figures. (see the sample for more information)
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Try to complete your construction in the most elegant manner possible.
One sketch per team of 2 – you should always work on the same construction at the same time
if you are in class. You may divvy up problems to work on between the computer lab days.
*Note: In each case, you are first given a figure with certain properties. You should construct this figure
first according to the given information. Then, you will construct the shape equivalent to your given
figure.
1) Given an arbitrary triangle construct an equivalent isosceles triangle
2) Given an arbitrary triangle construct an equivalent kite.
3) Given an arbitrary kite, construct an equivalent non-square rhombus
4) Given a rhombus with opposite angles that measure 60 degrees, construct an equivalent regular
hexagon
5) Given a regular pentagon, construct an equivalent right trapezoid.
6) Given a non- isosceles trapezoid, construct a rhombus with half the area.
7) Given a scalene quadrilateral, construct a triangle with half the area.
8) Construct two squares whose areas are in the ratio 2/1
9) Given two non-congruent squares, construct a third square whose area is the difference of the
areas of the first two.
10) Given an arbitrary triangle, construct a second triangle with congruent corresponding angles so
that the area is half of the first triangle