Page 2: Advanced Triangle Classification and Algebraic Solutions

This page delves into more complex triangle classifications and introduces algebraic problem-solving methods for finding triangle sides.

Example: Problem 1 demonstrates solving for x and y in an equilateral triangle where sides are expressed as algebraic expressions: 3x+1, 6x-45, and 18y-41

Highlight: The page introduces solving for triangle sides with algebra using properties of isosceles and equilateral triangles

Definition: In an isosceles triangle, two sides are congruent, and their corresponding angles are also congruent

Page 3: Practice Problems and Applications

This page provides comprehensive practice in classifying triangles by angles and sides through various examples and exercises.

Example: Problem 1 shows a triangle with angles 73°, 73°, and 34°, classified as an isosceles acute triangle

Highlight: The exercises incorporate both angle measurements and side lengths to provide complete triangle classification practice

Vocabulary: Bisector refers to a line that divides an angle or segment into two equal parts

Page 4: Advanced Algebraic Triangle Problems

This page focuses on complex algebraic problems involving triangle sides and their relationships.

Example: An equilateral triangle problem where ST = 2x-1, SU = 5x-37, and TU = x+11

Highlight: The problems demonstrate how to use algebraic equations to solve for unknown side lengths in isosceles and equilateral triangles

Definition: In an equilateral triangle, all sides must be equal and all angles must be 60°

Page 1: Triangle Classification Fundamentals

This page introduces the fundamental concepts of classifying triangles by angles and sides. The content is organized into clear sections with visual examples and definitions.

Definition: Triangles can be classified by angles into three categories: acute (all angles < 90°), obtuse (one angle > 90°), and right $one angle = 90°$

Vocabulary: Equiangular triangles have three congruent angles, each measuring 60°

Example: The diagram shows various triangles labeled ABDE (obtuse), ACFE (acute), and AJKN (equilateral)

Highlight: When classifying triangles by sides, they can be equilateral (3 congruent sides), isosceles (2 congruent sides), or scalene (no congruent sides)