section 3.2 three ways to prove triangles congruent
DESCRIPTION
Section 3.2 Three Ways to Prove Triangles Congruent. By: Audra Nealon , Cierra Beck, Abby Pipcho *All figures not drawn to scale*. Included Angles and Sides. Included Angles. Included angles are formed when two lines meet at a vertex and form an angle. - PowerPoint PPT PresentationTRANSCRIPT
Section 3.2Three Ways to Prove Triangles Congruent
By: Audra Nealon, Cierra Beck, Abby Pipcho*All figures not drawn to scale*
Included Angles and Sides
A
BC
Included AnglesIncluded angles are formed when two lines meet at
a vertex and form an angle. Ex. is the included angle of and
Included SidesIncluded sides are formed when two angles share a
common side. Ex. is the included side of andCB C B
A CA AB
The SSS PostulateIf there exists a correspondence between the vertices
of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.
A
B C
Z
X Y
ZXYABC
Example Proof
Statements Reasons
A
BC
D
Given: C is the midpoint of
ABAD BD
Prove ABCADC
1.
2. C is the midpoint of
3.
4.
5.
1. Given
2. Given
3. If a point is the midpoint of a seg, then it divides the seg. into two congruent segs.
4. Reflexive
5. SSS (1, 3, 4)
ABAD BD
CBDC
ACAC
ABCADC
The SAS PostulateIf there exists a correspondence between the vertices of two triangles such that two sides and the included angle
of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are
congruent.
ZXYABC
A
B C
Z
X Y
Example Proof
Statements Reasons
A
B
CD
Given:
ABDC
Prove CBAADC
1.
2.
3.
4.
5. and are right angles
6.
7.
1. Given
2. Given
3. Given
4. Reflexive
5. lines form right angles
6. All right angles are congruent
7. SAS (1, 4, 6)
ACAC
ACBA
ACDC
ABDC
ACBA
ACDC
DCA BAC BACDCA
CBAADC
The ASA PostulateIf there exists a correspondence between the vertices of two triangles such that two angles
and the included side of one triangle are congruent to the corresponding parts of the
other triangle, the two triangles are congruent.
ZXYABC
A
B C
Z
XY
Example Proof
Statements Reasons
A B
C
D
Given:
AE
Prove: EBCADC
1.
2. C is the midpoint of
3.
4.
5.
1. Given
2. Given
3. If a point is the midpoint of a seg, then it divides the seg into two congruent segs.
4. Vertical angles are congruent
5. ASA (1,3,4)
AE
BCEDCA
E
C is the midpoint of
AE
AE
CEAC
EBCADC
Practice ProofsGiven: ADAE
ACAB Prove: ABEACD
Given:
EF
EDBF
CFAE
CDAB
Prove: CFDABE
T
Given: RT bisects SRA
bisectsTR STA
Prove: ATRSRT
A
BC
DE
F
A
B
C
D
S
A
R
23
1
Answer to Proof #1 A
B
DE
F
Statements Reasons
1.
2.
3.
4.
1. Given
2. Given
3. Reflexive
4. SAS (1, 2, 3)
ADAE
ACAB
C
AA ABEACD
Which Triangles are the coldest?
ICE-sosceles triangles!
Answer to Proof #2 A
B
C
DF E
Statements Reasons1. Given
2. Addition
3. Given
4. Given
5. SSS (2, 3, 4)
1.
2.
3.
4.
5.
EDBF
FDBE
CFAE
CDAB
CFDABE
What did the triangle say to the circle?
Your life seems so pointless!!
Answer to Proof #3S
A
R
T
Statements Reasons1.
2.
3.
4.
5.
6.
1. Given
2. Given
3. If a ray bisects an angle, then it divides the angle into two congruent angles.4. Same as 3
5. Reflexive
6. ASA (3, 4, 5)
RT bisects SRATR bisects STA
ARTSRT
ATRSTR RTRT
ATRSRT
Why are only three sides to a triangle?The fourth side wanted to be a square!
Works Cited"Included Angle Definition - Math Open
Reference." Table of Contents - Math Open Reference. Web. 15 Jan. 2011.
“Included Side Definition - Math Open Reference.” Table of Contents - Math Open Reference. Web. 15 Jan. 2011.
Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, IL: McDougal, Littell, 1991.