# G.5 - Triangle Inequalities

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

a)  ordering the sides by length, given angle measures;

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

c)  determining whether a triangle exists;

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

### 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

2016 VDOE Curriculum Framework - G.5 Understanding

·  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

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

·  G.5a1  Order the sides of a triangle by their lengths when given information about the measures of the angles.

·  G.5b1  Order the angles of a triangle by their measures when given information about the lengths of the sides.

·  G.5c1  Given the lengths of three segments, determine whether a triangle could be formed.

·  G.5d1  Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie.

·  G.5abcd1  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: Jul 30, 2019