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EXAMPLE 3

GIVEN. CE BD ,. ∠ CAB CAD. ABE ADE. PROVE. EXAMPLE 3. Write a flow proof. In the diagram, CE BD and ∠ CAB CAD. ABE ADE. Write a flow proof to show. EXAMPLE 4. Standardized Test Practice.

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EXAMPLE 3

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  1. GIVEN CE BD, ∠ CAB CAD ABEADE PROVE EXAMPLE 3 Write a flow proof In the diagram,CE BDand∠ CAB CAD. ABEADE Write a flow proof to show

  2. EXAMPLE 4 Standardized Test Practice

  3. The locations of tower A, tower B, and the fire form a triangle. The dispatcher knows the distance from tower A to tower Band the measures of Aand B. So, the measures of two angles and an included side of the triangle are known. EXAMPLE 4 Standardized Test Practice By the ASA Congruence Postulate, all triangles with these measures are congruent. So, the triangle formed is unique and the fire location is given by the third vertex. Two lookouts are needed to locate the fire.

  4. EXAMPLE 4 Standardized Test Practice ANSWER The correct answer is B.

  5. ANSWER AAS Congruence Theorem. for Examples 3 and 4 GUIDED PRACTICE In Example 3, suppose ABEADEis also given. What theorem or postulate besides ASA can you use to prove that ABEADE?

  6. What If?In Example 4, suppose a fire occurs directly between tower B and tower C. Could towers B and C be used to locate the fire? Explain ANSWER No triangle is formed by the location of the fire and towers, so the fire could be anywhere between towers B and C. for Examples 3 and 4 GUIDED PRACTICE

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