Download Warm-Up Exercises

Warm-Up Exercises
Tell whether the pair of triangles is congruent or not
and why.
2. ABE and CBD
1.
ANSWER
Yes; HL
Thm.
ANSWER
SAS
Post.
Lesson 4.6 ASA and AAS
The side of a triangle that falls between two given angles is called the
included side of the angles. It is the one side common to both angles.
___________
C
AC is the included
side of A and C
CB is the included
side of C and B
A
B
AB is the included
side of A and B
You can show that two triangles are congruent by using two
_________
angles and
the included
____________
side of the triangles.
Angle-Side-Angle
angles and the ______________
If two
___________
included side of one triangle are
congruent to the corresponding angles and included side of
another triangle, then the triangles are congruent.
S
B
Postulate 5-3
ASA
Postulate
A
C
R
If A  R and AC  RT and C  T
then ΔABC  ΔRST
T
Warm-Up Exercises
Lesson 4.6: ASA & AAS
• ASA Postulate – If two angles and the
included side of one triangle are congruent
to two angles and the included side of
another triangle, then the triangles are
congruent.
ABC  DEF ASA
QRS  POS ASA
Angle-Angle-Side
CA and CB are the nonincluded
sides of A and B
C
A
B
You can show that two triangles are congruent by using two
_________
angles and
a ________________.
nonincluded side
AAS
If two
_________
of one triangle are
nonincluded side
anglesand a ______________
congruent to the corresponding two angles and nonincluded
side of another triangle, then the triangles are congruent.
S
B
Theorem 5-4
AAS
Theorem
A
C
R
If A R and C  T and CB  TS
then ΔABC  ΔRST
T
Warm-Up Exercises
AAS
• AAS – If two angles and a nonincluded side of
one triangle are congruent to the corresponding
two angles and side of a second triangle, the
two triangles are congruent
ABC  DEF AAS/SAA
HIJ  KIJ AAS/SAA
ASA and AAS
ΔDEF and ΔLNM have one pair of sides and one pair of angles
marked to show congruence.
What other pair of angles must be marked so that the two triangles are
congruent by AAS?
If F and M are marked congruent, then FE and MN would be
Included sides.
However, AAS requires the nonincluded sides.
D
Therefore, D and L must be marked.
L
M
F
E
N
Summary: Proving Triangles are
Congruent
• Ways that do not work:
• Ways that work:
–
–
–
–
SSS
SAS
ASA
AAS/SAA
– AAA
– SSA (The bad word
doesn’t work!)
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.
AAS
No
Congruence
ASA
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
SOLUTION
STATEMENTS
REASONS
S
U
Given
RS
UV
Given
RTS
UTV
RST  VUT
Vertical angles are
congruent
AAS
Warm-Up3Exercises
EXAMPLE
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
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.
Daily
Homework
Quiz
Warm-Up
Exercises
Tell whether each pair of triangle are congruent by
SAS, ASA, SSS, AAS or HL. If it is not possible to prove
the triangle congruent, write not necessarily
congruent.
1.
ANSWER
ASA .
Daily
Homework
Quiz
Warm-Up
Exercises
Tell whether each pair of triangle are congruent by
SAS, ASA, SSS, AAS or HL. If it is not possible to prove
the triangle congruent, write not necessarily
congruent.
2.
ANSWER
not necessarily congruent .
Daily
Homework
Quiz
Warm-Up
Exercises
Write flow proof.
Given : BD bisects ABC,
Prove :
ABD
CBD
3.
A
C
Daily
Homework
Quiz
Warm-Up
Exercises
ANSWER