Math - 2019-20

5.13 - Classify and Investigate Triangles

The student will

a)  classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles; and

b)  investigate the sum of the interior angles in a triangle and determine an unknown angle measure. 


Adopted: 2016

BIG IDEAS

  • So that when architects and construction workers are designing and building structures they can use strong triangular foundations
  • So that engineers can create triangular structures when designing buildings, landscapes, or bridges
  • So that an artist can include triangular shapes with their abstract art
  • So that when we use Tangrams we can classify them using their correct name

UNDERSTANDING THE STANDARD

  • Angles can be classified as right, acute, obtuse, or straight according to their measures.

  • A triangle can be classified as right, acute, or obtuse according to the measure of its largest angle.
  • Triangles may also be classified according to the measure of their sides, e.g., scalene (no sides congruent), isosceles (at least two sides congruent) and equilateral (all sides congruent).
  • An equilateral triangle (with three congruent sides) is a special case of an isosceles triangle (which has at least two congruent sides). 
  • Triangles can be classified by the measure of their largest angle and by the measure of their sides (i.e., an isosceles right triangle).

  • Congruent sides are denoted with the same number of hatch (or hash) marks on each congruent side.
  • A right angle measures exactly 90 degrees.
  • An acute angle measures greater than zero degrees but less than 90 degrees.
  • An obtuse angle measures greater than 90 degrees but less than 180 degrees.
  • A straight angle measures exactly 180 degrees.
  • A right triangle has one right angle.
  • An obtuse triangle has one obtuse angle.
  • An acute triangle has three acute angles.
  • A scalene triangle has no congruent sides.
  • An isosceles triangle has at least two congruent sides.
               
  • An equilateral triangle has three congruent sides.  All angles of an equilateral triangle are congruent and measure 60 degrees. 

ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

  • Classify triangles as right, acute, or obtuse. (a)
  • Classify triangles as equilateral, scalene, or isosceles. (a)
  • Compare and contrast the properties of triangles. (a)
  • Identify congruent sides and right angles using geometric markings to denote properties of triangles. (a)
  • Use models to prove that the sum of the interior angles of a triangle is 180 degrees, and use that relationship to determine an unknown angle measure in a triangle. (b) 

KEY VOCABULARY

Updated: May 29, 2019