EXAMPLE 3
Write a flow proof
In the diagram, CE
BD and  CAB
Write a flow proof to show
GIVEN
PROVE
CE
BD,  CAB
ABE
ADE
ABE
CAD
CAD.
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
ANSWER
The correct answer is B.
for Examples 3 and 4
GUIDED PRACTICE
3.
In Example 3, suppose ABE
ADE is also
given. What theorem or postulate besides ASA
ABE
ADE?
can you use to prove that
SOLUTION
STATEMENTS
REASONS
ABE
ADE
AEB
AED
Both are right
angle triangle.
BD
ABE
DB
ADE
Given
Definition of right
triangle
Reflexive Property of
Congruence
AAS Congruence Theorem
GUIDED PRACTICE
4.
for Examples 3 and 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.
GUIDED PRACTICE
for Examples 3 and 4
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.