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Download Geometry Section 5.7 Using Congruent Triangles
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Transcript
Geometry Section 5.7 Using Congruent Triangles What you will learn: 1. Use congruent tringles 2. Prove constructions Since congruent polygons have exactly the same size and shape, it stands to reason that corresponding parts of congruent triangles must be congruent (CPCTC). So if you can prove two triangles congruent, you can then state that any pair of corresponding angles or sides are congruent and use CPCTC as the reason. 1) FE ET , UT ET , F U , FE UT 1)Given 2)E & T are right angles 2)Def. of Perpendicular 3)E T 3)Right Angles Cong. Theorem )FLE ULT 4)ASA Cong. Theorem )FLE ULT )CPCTC 1)TV SU , T is the midpoint of SU 1)Given 2)STV & UTV are Rt. angles 2)Def. of Perpendicular 3)Rt. Angles Cong. Theorem 4)Def. of midpoint 5)Reflexive Prop. 6) SAS Congruence Theorem 3)STV UTV 4) ST TU 5)VT VT )SVT UVT )SVT UVT )CPCTC )VT bisects SVU )Def. of bisects Recall the steps involved in constructing an angle congruent to a given angle. Because we use the same radius on our compass, AC AB DE DF Because we use the same radius on our compass, BC EF ACB DFE by SSS A D by CPCTC HW: Do the proofs on the back of this page.