Write and solve equations that represent diagrams

Learning Objectives Translate geometric properties from diagrams into algebraic equations. Identify unknown variables in diagrams representing lengths, angles, or other quantities. Formulate linear and quadratic equations based on geometric relationships like perimeter, area, and angle sums. Solve the resulting linear and quadratic equations for the unknown variable. Substitute the solution back into the diagram's expressions to find actual lengths or angles. Verify the reasonableness of a solution in the context of the geometric diagram. Ever seen a blueprint and wondered how architects know the exact measurements for a weirdly shaped room? 📐 It all starts by turning pictures into math! This tutorial will teach you how to look at a diagram, translate it into an algeb...

TermDefinitionExample VariableA symbol, usually a letter like 'x', that represents an unknown numerical value in a diagram.In a rectangle, the width is labeled 'x' and the length is labeled 'x + 5'. Algebraic ExpressionA mathematical phrase that can contain ordinary numbers, variables, and operators. It represents a single value.The expression for the length of a fence post is '2x - 3' meters. EquationA statement that asserts the equality of two expressions. It's what you solve.If the perimeter of a square with side 'x' is 20, the equation is '4x = 20'. Geometric PropertyA rule or characteristic that is always true for a particular shape or situation.A key property of triangles is that their interior angles always sum to 180...

Perimeter of a Polygon P = s_1 + s_2 + ... + s_n Use this when a problem gives you the total perimeter of a shape. You will add the expressions for all side lengths (s) and set them equal to the given perimeter (P). Area of a Rectangle A = l \times w Use this when a problem provides the total area (A) of a rectangle. You will multiply the expressions for the length (l) and width (w) and set the result equal to the given area. This often leads to a quadratic equation. Angle Sum of a Triangle \angle A + \angle B + \angle C = 180^{\circ} Use this for any triangle diagram where the angles are represented by algebraic expressions. Add the three expressions together and set the sum equal to 180. Pythagorean Theorem a^2 + b^2 = c^2 Use this exclusively for right-ang...