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Understanding Angles and Proofs in Geometry

This lesson focuses on solving and proving relationships involving angles through various concepts, including linear pairs, congruence, and vertical angles. Key checks include finding angle measures based on given conditions and completing proofs that demonstrate the relationships between angles. Students will engage with diverse examples, including quilts and geometric figures, to apply their understanding of complementary and supplementary angles. This interactive approach enhances comprehension of essential geometry principles.

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Understanding Angles and Proofs in Geometry

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  1. Lesson 2-8 Lesson Title Concept Checks

  2. Check 1-A Find m1 if m2 = 58 and mJKL = 162. A. 32 B. 94 C. 104 D. 116 Click the mouse button or press the Space Bar to display the answers.

  3. Check 2 Concept Check QUILTINGThe diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD. A. 20 B. 30 C. 40 D. 50

  4. Check 3 In the figure, NYR andRYA form a linear pair,AXY and AXZ form a linear pair, and RYA andAXZ are congruent. Prove that NYR and AXY are congruent.

  5. Check 3 Statements Reasons 1. NYR and RYA, AXY and AXZ form linear pairs. 1. Given 2. NYR and RYA are supplementary. AXY and AXZ are supplementary. 2. If two s form a linear pair, then theyaresuppl.s. 3. Given 3. RYA  AXZ ? 4. ____________ 4. NYR  AXY Which choice correctly completes the proof? Proof:

  6. Check 3 A. Substitution B. Definition of linear pair C. s supp. to the same  or to  s are . D. Definition of supplementary s

  7. Check 4 If A and Z are vertical angles and mA = 3b -23 and mZ = 152 – 4b, find mA and mZ mA = 38 and mZ = 52 A. B. C. D. mA = 52 and mZ = 52 mA = 25 and mZ = 25 mA = 52 and mZ = 38

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