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4.2 Congruence and Triangles. Prove two triangles congruence. Congruent triangles. Congruent triangles have congruent angles and sides. The angles and sides must correspond. Congruent corresponding sides and corresponding angles. Meaning AB = XY; BC = YZ; AC = XZ and. - PowerPoint PPT Presentation
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4.2 Congruence 4.2 Congruence and Trianglesand Triangles
Prove two triangles Prove two triangles congruencecongruence
Congruent triangles
Congruent triangles have congruent angles and sides.
The angles and sides must correspond. Congruent corresponding sides and
corresponding angles.Meaning AB = XY; BC = YZ; AC = XZ and
XYZABC
ZXYCABYZXBCAXYZABC
Name the congruent triangles
Make sure the letters are in the appropriate order.
Figures can be congruent
If the sides and angles of two figures correspond, then the two figures are congruent. NOLM ≈ YXWZ
ZMZYMN
WLWZLM
XOXWOL
YNYXNO
;
;
;
;
Figures can be congruent
If the sides and angles of two figures correspond, then the two figures are congruent. NOLM ≈ YXWZ
ZMZYMN
WLWZLM
XOXWOL
YNYXNO
;
;
;
;
91
86
113
6
9
125 y34 x
Solve for k
2287154 k
A
B
CD E
F
Which Triangles are congruent and why?
E
F
H
G
J
58
58
Which Triangles are congruent and why?
All the sides and angles are
congruent
E
F
H
G
J
58
58
JHGEFG
Given: , O is the midpoint of MQ and PN Prove:
PQMNQPMN //;
QPOMNO M N
O
P Q
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN
PQMNQPMN //;
QPOMNO M N
O
P Q
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ;
PO = NO
PQMNQPMN //;
QPOMNO M N
O
P Q
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of
midpoint PO = NO
PQMNQPMN //;
QPOMNO M N
O
P Q
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of
midpoint PO = NO
#3.
PQMNQPMN //;
QPOMNO M N
O
P Q
QOPMON
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of
midpoint PO = NO
#3. #3. Vert. angles ≈
PQMNQPMN //;
QPOMNO M N
O
P Q
QOPMON
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of
midpoint PO = NO
#3. #3. Vert. angles ≈#4.
PQMNQPMN //;
QPOMNO M N
O
P Q
QOPMON OMNOQPMNOOPQ ;
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of
midpoint PO = NO
#3. #3. Vert. angles ≈#4. #4. Alt. Int. Angles
≈
PQMNQPMN //;
QPOMNO M N
O
P Q
QOPMON OMNOQPMNOOPQ ;
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of midpoint
PO = NO#3. #3. Vert. angles ≈#4. #4. Alt. Int. Angles ≈#5.
PQMNQPMN //;
QPOMNO M N
O
P Q
QOPMON OMNOQPMNOOPQ ;
QPOMNO
Given: , O is the midpoint of MQ and PN Prove:#1. O is the midpt. of #1. Given
MQ and PN#2. MO = OQ; #2. Def. of midpoint
PO = NO#3. #3. Vert. angles ≈#4. #4. Alt. Int. Angles ≈#5. #5. All parts are congruent
PQMNQPMN //;
QPOMNO M N
O
P Q
QOPMON OMNOQPMNOOPQ ;
QPOMNO
Properties of congruent Triangles
ReflexiveSymmetricTransitive ( not substitution )
As any twin can tell you, even if they look alike does not make them the same person.
HomeworkHomeworkPage 206 – 210 Page 206 – 210 ##10 – 28 even, 10 – 28 even,
39, 42 – 56 even39, 42 – 56 even
Homework
Page 206 – 210 # 11 – 29 odd,
30 – 35, 57
