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1 Lesson Plan #037 Class: Geometry Date: Wednesday December 7th, 2016 Topic: Proving Triangles congruent by Hypotenuse Leg Aim: How do we prove triangles congruent using the Hypotenuse Leg Theorem? Objectives: Students will be able to use the Hypotenuse Leg Theorem HW #037: Do Now: Construct the angle bisector of ABC Note: PROCEDURE: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Go over the Do Now Assignment #1: Complete the proof below Statements ̅̅̅̅ ≅ ̅̅̅̅ ̅̅̅̅to G so that 𝑬𝑮 1) Extend 𝑫𝑬 𝑨𝑩 (𝒔. ≅ 𝒔. ) ̅̅̅̅ 2) Draw 𝑭𝑮 ̅̅̅̅ ≅ ̅̅̅̅ 3) 𝑩𝑪 𝑬𝑭(𝒔. ≅ 𝒔. ) 4)< 𝐵 and < 𝐷𝐸𝐹 are right angles ̅̅̅̅ ⊥ ̅̅̅̅ 5)𝑫𝑮 𝑬𝑭 6)< 𝐺𝐸𝐹is a right angle 7)< 𝐵 ≅< 𝐺𝐸𝐹 8)𝚫𝐀𝐁𝐂 ≅ 𝚫𝑮𝑬𝑭 ̅̅̅̅ 9)̅̅̅̅̅ 𝑨𝑪 ≅ 𝑮𝑭 10)̅̅̅̅̅ 𝑨𝑪 ≅ ̅̅̅̅ 𝑫𝑭 ̅̅̅̅ ̅̅̅̅ ≅ 𝑮𝑭 11)𝑫𝑭 12)<D ≅< 𝐺 13)< 𝐷𝐸𝐹 ≅< 𝐺𝐸𝐹(𝒂. ≅ 𝒂. ) 14)𝜟𝑫𝑬𝑭 ≅ 𝜟𝑮𝑬𝑭 15) 𝜟𝑨𝑩𝑪 ≅ 𝜟𝑫𝑬𝑭 (𝒂. ≅ 𝒂. ) (𝒔. ≅ 𝒔. ) (𝒂. ≅ 𝒂. ) Reasons 1)A line segment may be extended any required length. 2) A line segment can be drawn joining two points. 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 2 Theorem: Two right triangles are congruent if the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other [ℎ𝑦. 𝑙𝑒𝑔 ≅ ℎ𝑦. 𝑙𝑒𝑔] Online Interactive Activity: See Hypotenuse Leg in Action! http://www.mathopenref.com/congruenthl.html Assignment #2: Assignment #3: Prove Δ𝐴𝐵𝐷 ≅ Δ𝐴𝐶𝐷 Statements 1. Assignment #4: Reason 1. 3 On Your Own: Complete the proofs below Medial Summary: 1) Given two right triangles, aside from having congruent corresponding right angles, what else would you have to know to prove that the two right triangles are congruent? 4 2) 3) 4) 5) 6)