Transcript 3.2 Three Ways to Prove a Triangle Congruent

3.2 Three Ways to Prove a
Triangle Congruent
Kaylee Nelson
Period: 8
Included Angles and
Included Sides

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An included angle
is an angle made
by two lines with
a common vertex
An included side
is a side that links
two angles
together
Three Ways to Prove Triangles
Congruent
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Angle-Side-Angle (ASA)
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
The Angle – Side – Angle
Postulate

The Angle – Side - Angle postulate
states that if two angles and the
included side of one triangle are
congruent to two angles and the
included side of another triangle,
then these two triangles are
congruent.
Sample Problem (ASA)
A   X
AB  XY
B  Y
Since angle A is
congruent to angle
X, segment AB is
congruent to
segment XY, and
angle B is congruent
to angle Y, the
triangles are
congruent through
ASA.
The Side – Side – Side
Postulate

The Side – Side - Side postulate
states that if three sides of one
triangle are congruent to three sides
of another triangle, then these two
triangles are congruent.
Sample Problem (SSS)

Since segment ZX is
congruent to
segment CA,
segment XY is
congruent to
segment AB, and
segment YZ is
congruent to
segment BC, the
triangles are
congruent through
SSS
ZX  CA
XY  AB
YZ  BC
The Side – Angle – Side
Postulate

The Side - Angle - Side postulate
states that if two sides and the
included angle of one triangle are
congruent to two sides and the
included angle of another triangle,
then these two triangles are
congruent.
Sample Problem (SAS)

Since segment AC is
congruent to
segment ZX, angle
ACB is congruent to
angle XZY, and
segment CB is
congruent to
segment ZY, the
triangles are
congruent through
SAS
AC  ZX
ACB  XZY
CB  ZY
Practice Problem One
Given : AD  CD
B is midpt of AC
Conclusion : ΔABD  ΔCBD
Practice Problem Two
Given : 3  6
KR  PR
KRO  PRM
Prove : ΔKRM  ΔPRO
Practice Problem Three
Given : AC  AB
AE  AD
Conclusion : ΔADB  ΔAEC
Answer Key
Practice Problem One
1. AD  CD
2. B is midpoint of AC
3. AB  CB
4. BD  BD
5. ΔABD  ΔCBD
1. Given
2. Given
3. If a pt is the midpt of a seg,
it divides the seg into two
congruent segments
4. Reflexive property
5. SSS (1, 3, 4)
Practice Problem One
1. AD  CD
1. Given
2. B is midpoint of AC
2. Given
3. If a pt is the midpt of a seg,
it divides the seg into two
congruent segments
4. Reflexive property
5. SSS (1, 3, 4)
3. AB  CB
4. BD  BD
5. ΔABD  ΔCBD
Practice Problem Two
1. 3  6
2. 3 is supp to 4
3. 5 is supp to 6
4. 4  5
5. KR  PR
6. KRO  PRM
7. KRM  PRO
8. ΔKRM  ΔPRM
1. Given
2. If two s forms a straight 
(assumed from diagram) they are supp
3. Same as 2
4. s supp to  s are 
5. Given
6. Given
7. Subtractio n property
8. ASA (4, 5, 7)
Practice Problem Three
1. AC  AB
1. Given
2. Given
2. AE  AD
3. Reflexive property
3. A  A
4. ΔADB  ΔAEC 4. ASA (1, 2, 3)
Works Cited
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Morris, Vernon. "Proving Congruent Triangles." Math Warehouse. 28 May 2008
<http://www.mathwarehouse.com/copyright.php>.
Page, John. Math Open Reference. 2007. 28 May 2008 <http://www.mathopenref.com/index.html>.
Rhoad, Richard, George Milauskas, Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois:
McDougal, Littell & Company, 1991.