Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)

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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.
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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.
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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?
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