EXAMPLE 3 Write a flow proof In the diagram, CE BD and  CAB CAD. Write a flow proof to show ABE ADE GIVEN CE BD,  CAB CAD PROVE ABE ADE.

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EXAMPLE 3 Write a flow proof In the diagram, CE BD and  CAB CAD. Write a flow proof to show ABE ADE GIVEN CE BD,  CAB CAD PROVE ABE ADE

EXAMPLE 4 Standardized Test Practice

EXAMPLE 4 Standardized Test Practice The locations of tower A, tower B, and the fire form a triangle. The dispatcher knows the distance from tower A to tower B and the measures of A and B. So, the measures of two angles and an included side of the triangle are known. 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.

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

GUIDED PRACTICE for Examples 3 and 4 SOLUTION In Example 3, suppose ABE ADE is also given. What theorem or postulate besides ASA can you use to prove that 3. ABE ADE ? Given ABEADE Both are right angle triangle. Definition of right triangle AEBAED Reflexive Property of Congruence BD DB STATEMENTS REASONS AAS Congruence Theorem ABE ADE

GUIDED PRACTICE for Examples 3 and 4 4. 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 SOLUTION Proved by ASA congruence The locations of tower B, tower C, and the fire form a triangle. The dispatcher knows the distance from tower B to tower C and the measures of B and C. So, he knows the measures of two angles and an included side of the triangle.

By the ASA Congruence Postulate, all triangles with these measures are congruent. No triangle is formed by the location of the fire and tower, so the fire could be anywhere between tower B and C. GUIDED PRACTICE for Examples 3 and 4