<p><strong>Lesson Contents: Circle Theorems</strong></p> <p><strong>Download Includes:</strong></p> <ul> <li>A comprehensive PowerPoint lesson designed for interactive use with a clicker, mouse, or keyboard to navigate through animations and display fully animated and worked solutions.</li> </ul> <p><strong>Topic of Study: Circle Theorems</strong></p> <p><strong>Differentiated Objectives:</strong></p> <ol> <li> <p><em>Developing Learners will be able to:</em></p> <ul> <li>Apply circle theorems to find missing angles.</li> </ul> </li> <li> <p><em>Secure Learners will be able to:</em></p> <ul> <li>Justify, with reason, the circle theorems they apply to find missing angles.</li> </ul> </li> <li> <p><em>Excelling Learners will be able to:</em></p> <ul> <li>Solve unfamiliar problems using circle theorems.</li> </ul> </li> </ol> <p><strong>Main Components:</strong></p> <p>The main segment of the lesson unfolds with a step-by-step approach:</p> <ul> <li>Walked through examples demonstrate the application of circle theorems.</li> <li>Practice questions on accompanying worksheets progress from basic queries on the just-introduced theorem to exam-style questions utilizing each of the theorems previously introduced.</li> <li>All solutions are provided directly within the PowerPoint presentation for easy reference.</li> </ul> <p><strong>Circle Theorem Statements:</strong></p> <ol> <li> <p><em>Angles in the Same Segment:</em></p> <ul> <li>Angles in the same segment of a circle are equal.</li> </ul> </li> <li> <p><em>Opposite Angles in a Cyclic Quadrilateral:</em></p> <ul> <li>Opposite angles in a cyclic quadrilateral add up to 180 degrees.</li> </ul> </li> <li> <p><em>Angle at the Center:</em></p> <ul> <li>The angle at the center of a circle is twice any angle at the circumference subtended by the same arc.</li> </ul> </li> <li> <p><em>Angles in a Semi-Circle:</em></p> <ul> <li>Angles formed in a semi-circle are always right angles.</li> </ul> </li> <li> <p><em>Alternate Segment Theorem:</em></p> <ul> <li>An angle between a chord and a tangent is equal to the angle in the alternate segment.</li> </ul> </li> <li> <p><em>Tangent-Radius Perpendicularity:</em></p> <ul> <li>A radius at the point of tangency to a circle is perpendicular to the tangent.</li> </ul> </li> <li> <p>*Cyclic Quadrilateral Diagonals:</p> <ul> <li>The diagonals of a cyclic quadrilateral bisect each other at right angles.</li> </ul> </li> <li> <p><em>Chord Bisection:</em></p> <ul> <li>A chord that passes through the center of a circle is bisected by the circle into two equal parts.</li> </ul> </li> </ol> <p>This lesson is structured to empower learners at various levels, ensuring a comprehensive understanding of circle theorems and proficiency in their application across different scenarios.</p>

<p>There is a collection of resources which includes a variety of PPTs and PDFs that describe various GCSE graph objectives. These include:</p> <ol> <li>Plotting quadratic, cubic, reciprocal, and exponential curves</li> <li>Draw tangents to estimate the gradient of the curve.</li> <li>Solving equations using the graph of the function drawn.</li> <li>Asymptotes</li> </ol>

<p>There is a collection of PPTs included that cover the whole spectrum of strategies for solving quadratic equations, from factorization method to completing the square to utilizing the formula. It is intended to cover around 6-8 classes.</p>

<p>There is a set of PPTs supplied that cover the whole range of procedures that aid in the construction of linear, quadratic, and cubic sequences. It is intended to span around 4-5 lessons.</p>

<p>The PPT includes detailed explanation of the plotting and interpretation of scatter diagram. The PPT is intended to cover around 2-3 lessons.</p>

<p>There is a collection of PPTs provided that cover the whole class covering histogram building, data comparison and interpretation using histograms. It is designed to cover around 2-3 lessons.</p>

<p>There is a collection of PPTs included that cover the whole spectrum of strategies for solving quadratic equations, from factorization method to completing the square to utilizing the formula. It is intended to cover around 6-8 classes.</p>

<p>There is a collection of PPTs provided that cover the whole range of procedures for simplifying algebraic fractions, adding and subtracting fractions, and solving algebraic fraction-based problems. It is designed to cover about 4-5 lessons.</p>

<p>This resource is a set of PowerPoint presentations that illustrate the surface area and volume of a hemisphere. It is meant to cover three to four lessons.</p>