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Proving Triangles are Congruent. Given: ,. Prove:. There should be 5 statements with justification. Statement #1 is given. Statement # 2 is also given. Statement # 3 Reflexive Property Triangles Sharing A Side Vertical Angles Triangles With angles facing each other Mid-Point - PowerPoint PPT Presentation
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Proving Triangles are CongruentThere should be 5 statements with
justification
• Statement #1 is given.• Statement # 2 is also given.• Statement # 3
– Reflexive Property• Triangles Sharing A Side
– Vertical Angles• Triangles With angles facing each other
– Mid-Point• Mid-point is given, triangles connected
by a point.
• Statement # 4 Congruence Postulates
– SSS, SAS, AAS, ASA
• Statement # 5 (CPCTC)– Congruent Parts of Congruent Triangles
are Congruent
Statements Justifications
1. Given
2. Given
3. Reflexive Property
SAS Congruency Postulate4.
CPCTC5.
Given: , Prove:
𝐶
𝐵
𝐴
𝐷
Prove:
M
AN
I
Given: MA IA
Given: MN IN
IM
Statement Justification
MA IA.)1
.)2 MN IN
.)3
.)4
.)5
Given
Wha
t is
given
? HIN
T:
Mar
kings
Wha
t is
given
? HIN
T:
Mar
kings
Given
Whi
ch
Prop
erty
is
sh
own?
JU
STIF
Y
NA NA Reflexive Property
Wha
t co
ngru
ence
po
stul
ate
wor
ks?
MAN IAN SSS
Wha
t can
w
e co
nclu
de?
IM CPCTC
Prove: P
Statement Justification
Prove: ∠𝑄≅∠𝑁 Prove: ∠𝐴≅∠𝐶
Prove:
AN
Given: B is the midpoint of
Statement Justification
.)1
.)2
.)3
.)4
.)5
Given
Given (Definition of Midpoint)
Vertical Angles
SAS
CPCTC
𝐴𝐷 ≅ 𝐸𝐶
𝐴𝐵 𝐸𝐵𝐷𝐵 𝐶𝐵
∠𝐷𝐵𝐴 ∠𝐶𝐵𝐸
∆𝐷𝐵𝐴 ∆𝐶𝐵𝐸𝐴𝐷 ≅ 𝐸𝐶
Prove: Given: R is the midpoint of
Statement Justification
.)1
.)2
.)3
.)4
.)5
Given
Given (Definition of Midpoint)
Vertical Angles
ASA
CPCTC
∠𝑇 ≅∠𝑃
∠𝑆 I
𝑆𝑅 𝐼𝑅
∠𝑇𝑅𝑆 ∠𝑃𝑅𝐼
∆ 𝑇𝑅𝑆 ∆ 𝑃𝑅𝐼
T
IR
P
S
∠𝑇 ≅∠𝑃
Prove:
Statement Justification
TI
R
P
SHOW ALL YOUR WORK
Prove:
Statement Justification
SHOW ALL YOUR WORK
Prove: ∠𝐷≅∠𝐸 Prove: ∠𝐺≅∠ I
Prove: ∠𝑂 ≅∠𝑃 Prove: ∠𝐿≅∠ 𝐽
Prove: ∠𝑆≅∠𝑊Given: U is the midpoint of
Prove: ∠𝑋 ≅∠𝑅
T
R
Prove:
Statement Justification
I
P
SHOW ALL YOUR WORK
T
R
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