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Warm-Up Exercises
Tell whether the pair of triangles is congruent or not
and why.
ANSWER
Yes; HL
Thm.
Warm-Up1Exercises
EXAMPLE
Identify congruent triangles
Can the triangles be proven congruent with the
information given in the diagram? If so, state the
postulate or theorem you would use.
SOLUTION
a.
The vertical angles are congruent, so two pairs of
angles and a pair of non-included sides are
congruent. The triangles are congruent by the AAS
Congruence Theorem.
Warm-Up1Exercises
EXAMPLE
Identify congruent triangles
b.
There is not enough information to prove the
triangles are congruent, because no sides are
known to be congruent.
c.
Two pairs of angles and their included sides are
congruent. The triangles are congruent by the ASA
Congruence Postulate.
Warm-Up2Exercises
EXAMPLE
Prove the AAS Congruence Theorem
Prove the Angle-Angle-Side Congruence Theorem.
GIVEN
PROVE
A
D,
ABC
C
DEF
F, BC
EF
Warm-Up
Exercises
GUIDED
PRACTICE
1.
for Examples 1 and 2
In the diagram at the right, what
postulate or theorem can you use to
RST
VUT ? Explain.
prove that
ANSWER
AAS;
RTS and
VTU are congruent because they
are vertical angles.
Warm-Up
Exercises
GUIDED
PRACTICE
2.
for Examples 1 and 2
Rewrite the proof of the Triangle Sum Theorem
as a flow proof.
GIVEN
PROVE m
ABC
1+m
2+m
3=
180°
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Warm-Up3Exercises
EXAMPLE
Write a flow proof
In the diagram, CE
BD and
Write a flow proof to show
GIVEN
PROVE
CE
BD,
ABE
CAB
ADE
CAB
ABE
CAD
CAD.
ADE
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
Warm-Up4Exercises
EXAMPLE
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.
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
ANSWER
The correct answer is B.
Warm-Up
Exercises
GUIDED
PRACTICE
3.
for Examples 3 and 4
In Example 3, suppose ABE
ADE is also
given. What theorem or postulate besides ASA
ABE
ADE?
can you use to prove that
ANSWER
AAS Congruence Theorem.
Warm-Up
Exercises
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
ANSWER
No; no triangle is formed by the location of the fire
and towers, so the fire could be anywhere between
towers B and C.
Daily
Homework
Quiz
Warm-Up
Exercises
Tell whether each pair of triangles is congruent by
SAS, ASA, SSS, AAS or HL. If it is not possible to prove
the triangles congruent, write not necessarily
congruent.
1.
ANSWER
ASA
Daily
Homework
Quiz
Warm-Up
Exercises
Tell whether each pair of triangles is congruent by
SAS, ASA, SSS, AAS or HL. If it is not possible to prove
the triangles congruent, write not necessarily
congruent.
2.
ANSWER
not necessarily congruent
Daily
Homework
Quiz
Warm-Up
Exercises
3.
Write a flow proof.
Given : BD bisects ABC,
Prove :
ABD
CBD
A
C
Daily
Homework
Quiz
Warm-Up
Exercises
ANSWER