#### 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*