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.

• 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.
  

·  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.

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. 

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

2016 Word Wall Cards