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Part A: Different Triangles
Part B: Linkage-Strip Constructions
Part C: Building Towers
Homework
In this session, you will build triangles and quadrilaterals to explore their properties. Classification is an important part of geometry and other areas of mathematics. By creating and manipulating triangles and quadrilaterals, you will develop a sense of logical classifications and how different figures are related.
For information on required and/or optional materials for this session see Note 1 below.
In this session, you will learn the following:
Altitude: An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.
Perpendicular Bisector: The perpendicular bisector of a line segment is perpendicular to that segment and bisects it; that is, it goes through the midpoint of the segment, creating two equal segments.
Acute Triangle: An acute triangle is a triangle with all three angles less than 90°.
Congruent: Two figures are congruent if all corresponding lengths are the same, and if all corresponding angles have the same measure. Colloquially, we say they “are the same size and shape,” though they may have different orientation. (One might be rotated or flipped compared to the other.)
Equilateral Triangle: An equilateral triangle is a triangle with three equal sides.
Isosceles Triangle: An isosceles triangle is a triangle with two equal sides.
Obtuse Triangle: An obtuse triangle is a triangle with one angle more than 90°.
Right Triangle: A right triangle is a triangle with one right (90°) angle.
Scalene Triangle: A scalene triangle is a triangle with all three sides unequal.
Side-Angle-Side (SAS) Congruence: Side-angle-side (SAS) congruence states that if any two sides of a triangle are equal in length to two sides of another triangle and the angles bewteen each pair of sides have the same measure, then the two triangles are congruent; that is, they have exactly the same shape and size.
Side-Side-Side (SSS) similarity: he side-side-side (SSS) similarity test says that if two triangles have all three pairs of sides in proportion, the triangles must be similar.
Similar Triangles: Similar triangles are triangles that have the same shape but possibly different size. In particular, corresponding angles are congruent, and corresponding sides are in proportion.
Triangle Inequality: The triangle inequality says that for three lengths to make a triangle, the sum of the lengths of any two sides must be greater than the third length.
Part A Notes: Different Triangles
Part B Notes: Linkage-Strip Constructions
Part C Notes: Building Towers
Materials Needed
You can make your own linkage strips from stiff paper with evenly spaced holes and paper fasteners, or you can purchase them from ETA/Cuisenaire under the name polystrips.
For homework, you’ll also need a ruler marked in inches and a protractor. Collect this set of materials for each group or individual working alone.
Polystrips
ETA/Cuisenaire
500 Greenview Court
Vernon Hills, IL 60061
800-445-5985 847-816-5050
800-875-9643 847-816-5066 (fax)
(Product not available online)