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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?
GivenABE ADE
Both are right angle triangle.
Definition of right triangle
AEB AED
Reflexive Property of Congruence
BD DB
STATEMENTS REASONS
AAS Congruence TheoremABE 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