## Monday, May 16, 2011

### Second of Three Triangular Treatises

Friday I talked about triangles and provided some animated illustrations. In the process, I discovered that we had a surplus of appearances of the word TRIANGLE in our Sixth grade Excel Math curriculum. Had we taught the subject too often? Had we tested students to exhaustion?

I investigated this situation and learned it was due solely to a Triangle Reference Page which had adversely influenced the Adobe Acrobat word counter.

Triangular Pyramid (made of drinking straws)

I created the page about 4 years ago, and had forgotten about its existence. Here's some of the content, which you must admit is fairly triangle-dense in its vocabulary!

Parts and Terms used in Triangles
• An angle is the intersection of two line segments that share a common endpoint.
• Interior angle - measured inside the figure
• Exterior angle - measured outside the figure
• Right angle - 90 degrees
• Acute angle - less than 90 degrees but greater than zero
• Obtuse angle - greater than 90 degrees but less than 180 degrees
• Reflex angle - greater than 180 degrees
• Base - any one chosen side of a triangle, normally on the bottom
• Sides - the two non-base edges of a triangle
• Altitude - the height of a triangle, measured at a right angle from the base to the highest point and used in calculating the area of a triangle (1/2 base x height)
Types of Triangles (described by their sides)
• Scalene triangle - triangle with no congruent sides
• Isosceles triangle - triangle with at least 2 congruent sides
• Equilateral triangle - triangle with 3 congruent sides
Types of Triangles (described by their angles)
• Acute triangle - triangle with three acute angles
• Obtuse triangle - triangle with one obtuse angle (and 2 acute angles)
• Right triangle - triangle with one right angle (and 2 acute angles)
• Equiangular triangle - triangle with 3 congruent angles (pronounced ee-qwee-ang-you-lar; try saying Equiangular triangle quickly 3 times!)
• 30 - 60 - 90 triangle - triangle with 3 specific angles
• 45 - 90 - 45 triangle - triangle with a right angle and two equal angles
• 60 - 60 - 60 triangle - an equiangular triangle
Angles and Triangles
• Supplementary angles are two angles that add up to 180 degrees. Can triangles have supplementary angles? (No, because the sum of all 3 angles is equal to 180 degrees.)
• Complementary angles are two angles that add up to 90 degrees. Can triangles have complementary angles? (Right triangles can.)
• Vertical angles are the angles formed by two intersecting lines. Can triangles have vertical angles? (No. Plane figures are formed by line segments, not intersecting lines.)
• Adjacent angles share a vertex and a common side but do not overlap. Can triangles have adjacent angles? (No, angles do not have common vertexes in a triangular figure. A triangular pyramid could have adjacent angles.)
• Interior angles are measured inside the figure. The sum of the 3 interior angles of a triangle is always 180 degrees.
• Exterior angles are measured outside the figure. The sum of the 3 exterior angles of a triangle is always 900 degrees. Are the exterior angles of a triangle always reflex angles? (Yes)
• The sum of the degrees of the exterior angles and interior angles is 1080 degrees. That's the same as the sum of the degrees found in 3 circles. Is there any meaning to this observation? (I don't know)