# 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.

### 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: Mar 06, 2019