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4.6 Using Congruent Triangles
Corresponding parts of congruent triangles are congruent. *Special case of definition of congruent figures. *Used after proving triangles congruent. CPCTC
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Angles in a linear pair are ≡. Suppl. Of ≡ <s are ≡.
Statements Reasons 1. <1 ≡ <2 <ABC suppl. <1 <DEC suppl <2 3. < ABC ≡ < DEC 4. <ACB ≡ <DCE 5. ACB ≡ DCE . Given Angles in a linear pair are ≡. Suppl. Of ≡ <s are ≡. Vertical <s are ≡ . AAS ≡ CPCTC
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The triangles are congruent
by ASA. CPCTC says that AB= DE. If you can measure length of DE, then you will know the length of AB.
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The supplements of < 1 and <2 are congruent. DE is reflexive.
∆ DEB ≡ ∆ DEC by AAS. DB ≡ DC because of CPCTC. AD is reflexive. This makes ∆ ABD ≡ ∆ ACD by SAS.
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Geometry Page 257(1-14, 28, 41-43) Page 259 (18-24, 29-31, 33-35, 44-46)
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