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Inscribed Quadrilaterals: Angle Measures & Circle Intercepts

In this lesson, students will learn how to find the angles in inscribed quadrilaterals using the Inscribed Angle Theorem. They will also understand the concept of supplementary angles and the relationship between inscribed angles and intercepted arcs in a circle.

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Inscribed Quadrilaterals: Angle Measures & Circle Intercepts

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  1. Learning Objective We will determine1 how to find the angles that are Inscribed in the Quadrilaterals2. What are we going to do? What is determine means?_____. CFU Activate Prior Knowledge Inscribed Angle Theorem Inscribed Angle Theorem states that the measure of an inscribed angle is equal to half the measure of its intercepted arc. Activate Prior Knowledge CFU On your whiteboard, Students, you already know how to find inscribed angles in circle. Today, we will learn how to find the angles of Inscribed Quadrilaterals . Make Connection 1 Figure out 2 A four-sided figure. Vocabulary

  2. Concept Development CFU CFU Whiteboard: What is m∠Z? Explain how you found the measure. Pair-Share: What can you say about the diagonal XZ? Explain your answer. Since m∠X + m∠Z = 180° by the Inscribed Quadrilateral Theorem, then 60° + m∠Z = 180°, so m∠Z = 120°. XZ is a diameter of the circle because it is the chord of a 90° inscribed angle.

  3. Skill Development/Guided Practice In an inscribed quadrilateral, the opposite angles are supplementary to each other. Their measures add up to 180 .° This is based on the inscribed quadrilateral 1. On your whiteboard, In the figure, quadrilateral WXYZ is inscribed in the circle. 2. on your Whiteboard, find the angle measures of the quadrilateral.: • What is the sum of the opposite angle measures? __ • Write an equation using ∠G and ∠I • to solve for m.

  4. Skill Development/Guided Practice In an inscribed quadrilateral, the opposite angles are supplementary to each other. Their measures add up to 180 .° This is based on the inscribed quadrilateral 1. On your whiteboard, Find the value of y. 1. On your whiteboard, Find the measure of each angle of inscribed quadrilateral TUVW

  5. Relevance Reason #1: Constructing an Inscribed Square: Many designs are based on a square inscribed in a circle. It will also help you in Critique Reasoning and Thinking. Marcus said he thought some information was missing from one of his homework problems because it was impossible to answer the question based on the given information. The question and his work are shown. Critique Marcus’s work and reasoning. Relevance Reason #2: Knowing how to find angles Inscribed in the Quadrilaterals will help you do well on tests: (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..). The problem states the quadrilateral can be inscribed in a circle, which means that opposite angles are supplementary. He should have written two separate equations, each with only one variable, (x - 2) + (2x - 28) = 180 and (6z - 1) + (10z + 5) = 180 and used those equations to solve the problem.

  6. What did you learn today about how to find the angles Inscribed in the Quadrilaterals. Word Bank SUMMARY CLOSURE • Circle • Supplementary Angles • Inscribed Angle • Diameter • Quadrilaterals Today, I learned how:________________________________ ____________________________________________ ____________________________________________

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