45 Smartboard Notes and answers.notebook
1
September 17, 2013
Sep 1310:48 AM
Apply SSS and SAS to construct triangles and solve problems.
Prove triangles congruent by using SSS and SAS.
Objectives
Sep 1310:48 AM
In Lesson 43, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent.
The property of triangle rigidity gives you a shortcut for proving two triangles congruent. It states that if the side lengths of a triangle are given, the triangle can have only one shape.
45 Smartboard Notes and answers.notebook
2
September 17, 2013
Sep 1310:48 AM
For example, you only need to know that two triangles have three pairs of congruent corresponding sides. This can be expressed as the following postulate.
Sep 1310:48 AM
Example 1: Using SSS to Prove Triangle Congruence
45 Smartboard Notes and answers.notebook
3
September 17, 2013
Sep 1310:48 AM
Check It Out! Example 1
Statements Reasons
Given1. 1.
2. 2.
3. 3.
Sep 1310:48 AM
An included angle is an angle formed by two adjacent sides of a polygon.∠B is the included angle between sides AB and BC.
The SAS Postulate guarantees that if you are given the lengths of two sides and the measure of the included angles, you can construct one and only one triangle.
45 Smartboard Notes and answers.notebook
4
September 17, 2013
Sep 1310:48 AM
Example 2: Engineering Application
The diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ ≅ ∆VWZ.
Sep 1310:48 AM
Check It Out! Example 2
Use SAS to explain why ∆ABC ≅ ∆DBC.
45 Smartboard Notes and answers.notebook
5
September 17, 2013
Sep 1310:48 AM
Example 4: Proving Triangles Congruent
Given: BC ║ AD, BC ≅ AD
Prove: ∆ABD ≅ ∆CDB
Sep 1310:48 AM
Check It Out! Example 4
Given: QP bisects ∠RQS. QR ≅ QS
Prove: ∆RQP ≅ ∆SQP
45 Smartboard Notes and answers.notebook
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September 17, 2013
Sep 1311:17 AM
Assignment(p. 254) 7, 1317, 21, 33
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