Math - 2019-20
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.
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 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
· 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.
side, angle, triangle, order, angle measure, degree measure, range, segment,
included angle, included side, opposite side