#### Math - 2017-18

# G.5 and *G.5 - Triangle Inequalities

**G.5** The student, given information concerning the lengths of sides and/or
measures of angles in triangles, will

a) **order** the sides by length, given the angle
measures;

b) **order **the angles by degree measure, given the
side lengths;

c) **determine **whether a triangle exists; and

d) **determine **the range in which the length of
the third side must lie.

These concepts will be considered in the context of real-world situations.

G.5The student, given information concerning the lengths of sides and/or measures of angles in triangles, willsolveproblems, including practical problems. This will includea)

orderingthe sides by length, given angle measures;b)

orderingthe angles by degree measure, given side lengths;c)

determiningwhether a triangle exists;d)

determiningthe range in which the length of the third side must lie.

**Bloom's Level:** Analyze

*Adopted: 2009*

### BIG IDEAS

- I can triangulate the location of a cell phone, design a
bicycle to hold maximum weight, tell if a ladder will stand level, and determine
the amount of wire required to make a coat hanger.

- I will realize that knowledge of
triangles can be helpful in solving real-world problems since triangles are one
of the basic shapes in our everyday surroundings, strong enough to withstand
pressure and force, and economical since they only have 3 sides.

### UNDERSTANDING THE STANDARD

- The longest side of a triangle is opposite the
largest angle of the triangle and the shortest side is opposite the smallest
angle.
- In a triangle, the length of two sides and the
included angle determine the length of the side opposite the angle.
- In order for a triangle to exist, the length of
each side must be within a range that is determined by the lengths of the other
two sides.

· The longest side of a triangle is opposite the largest angle of the triangle and the shortest side is opposite the smallest angle.

· In a triangle, the lengths of two sides and the included angle determine the length of the side opposite the angle.

· In order for a triangle to exist, the length of each side must be within a range that is determined by the lengths of the other two sides.

### ESSENTIALS

G.5a_{1}
**Order** the sides of a triangle
by their lengths when given the measures of the angles.

· G.5a_{1} **Order**
the sides of a triangle by their lengths when given information about the
measures of the angles.

G.5b_{1}
**Order** the angles of a
triangle by their measures when given the lengths of the sides.

· G.5b_{1} **Order**
the angles of a triangle by their measures when given information about the
lengths of the sides.

G.5c_{1}
Given the lengths of 3 segments, **determine**
whether a triangle could be formed.

· G.5c_{1} Given the lengths of three segments, **determine** whether a triangle could be
formed.

G.5d_{1}
Given the length of 2 sides of a triangle, **determine** the range in which the length of the 3^{rd} side
must lie.

· G.5d_{1} Given the lengths of two sides of a triangle,
**determine** the range in which the
length of the third side must lie.

G.5_{2}
**Solve** the real-world problems
given information about the lengths of sides and/or measures of angles in
triangles.

· G.5abcd_{1} Given information about the lengths of sides
and/or measures of angles in triangles, **solve**
problems, including practical problems.

### KEY VOCABULARY

length,
side, angle, triangle, order, angle measure, degree measure, range, segment,
included angle, included side, opposite side

*Updated: Oct 27, 2017*