Page 2: Advanced Trapezoid Calculations and Isosceles Trapezoids

This page delves into more complex trapezoid problems, including calculations involving isosceles trapezoids and finding specific side lengths and heights.

Vocabulary: An isosceles trapezoid is a trapezoid where the non-parallel sides are equal in length.

Students are presented with problems that require them to find the height of a trapezoid with area and bases given. They also practice solving trapezoid problems that involve algebraic expressions for side lengths and angles.

Example: Problem 10 asks students to solve for x and y in an isosceles trapezoid where EH = 4x-27, FG = x + 9, EG = 3y + 19, and FH = 11y-21.

The page includes exercises on finding the height of a trapezoid without area, using only the given side lengths and algebraic relationships. Students must apply their knowledge of trapezoid properties and algebraic problem-solving skills to tackle these advanced problems.

Highlight: The ability to set up and solve systems of equations is essential for the more complex isosceles trapezoid problems on this page.

The homework concludes with problems that require students to find specific side lengths of trapezoids, reinforcing their understanding of trapezoid geometry and algebraic manipulation.

Page 1: Trapezoid Angle and Side Calculations

This page introduces students to various trapezoid problems and their solutions. The exercises focus on finding missing angle measures and side lengths in trapezoids using algebraic equations and geometric principles.

Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides.

The problems on this page require students to apply the trapezoid area formula and angle sum properties to solve for unknown variables. Students are challenged to use their knowledge of trapezoid properties to find missing angle measures in different scenarios.

Example: In problem 5, students must solve for x in the equation (14x-15) + 139 = 180, which represents the sum of angles in a trapezoid.

The exercises progressively increase in complexity, requiring students to apply multiple steps and combine different concepts to arrive at the correct solutions.

Highlight: Understanding the relationship between opposite angles in a trapezoid is crucial for solving these problems efficiently.