Triangle Proofs fill in Blanks

Claim:​ ΔADC≅ΔBDC

Context:​ (a)   , CD Bisects AB

Evidence: ​ (b)   by​ def of bisector

​ CD ≌ DC by​ (c)  

Explanation: ΔADC≅ΔBDC by​ (d)  

• AC ≅ CB
• ∠ACD ≅∠BCD
• reflexive property
• SAS
• SSS
• ASA
• AAS
• Vertical Angles
• alternate interior angles

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

CCSS.HSG.SRT.B.5

Claim:⊿ABC≅⊿DEC

Context: ​ ​ (a)   , C is the midpoint of BE and AD

Evidence:​ (b)   by definition of midpoint

AC≌DC by​ (c)  

Explanation: ⊿ABC≅⊿DEC by​ (d)  

• BA≅ED
• BC≌CE
• definition of midpoint
• SSS
• SAS
• Vertical Angles
• Reflexive Property
• AAS
• Alternate interior angles

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

​ Claim: ⊿ABC≌⊿ECD

Context:​ (a)   ​, ​​ (b)  

Evidence:​ (c)   by​ (d)  

Explanation: ⊿ABC≌⊿ECD BY​ (e)  

• BC≌DC
• AC ≌ EC
• ∠ACB ≌ ∠ECD
• Vertical Angles
• SAS
• Reflexive Property
• ∠ABC ≌ ∠CED
• Alternate Interior Angles
• AAS
• ASA

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

Claim:⊿WXZ≅⊿YZX

Context: WX∥YZ, ​ (a)  

Evidence: ​ (b)   by
(c)   , ​ (d)   by ​Reflexive Property

Explanation: ⊿WXZ≅⊿YZX by​ (e)  

• WX≅YZ
• ∠WXZ≅∠YZX
• Alternate Interior
• ZX≅XZ
• SAS
• Vertical Angles
• ∠W≅∠Y
• ASA
• SSS

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

CCSS.HSG.CO.C.9

CCSS.HSG.SRT.B.5

Claim RQ≅QS

Context: TQ bisects ∠RTS, TQ⊥RS

Evidence:​ (a)   by def of bisector

​ (b)   by def of ⊥

​ (c)   by​ (d)  

Explanation: ⊿RTQ≅STQ by​ (e)   so, RQ≅QS by ≅parts of ⊿

• ∠RTQ ≅∠STQ
• ∠RQT≅∠SQT
• TQ≅TQ
• Reflexive Prop.
• ASA
• SSS
• AAS
• RT≅TR
• vertical angles
• alt. interior angles

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

CCSS.HSG.SRT.B.5

Claim: ⊿ABE≅⊿CDE

Context: AB∥CD AE≅CE

Evidence: ​ (a)   by​ (b)   ,∠AEB≅∠DEC by​ (c)  

Explanation: ⊿ABE≅⊿CDE by ​ (d)  

• ∠A≅∠C
• Alternate Interior Angles
• Vertical Angles
• ASA
• SSS
• SAS
• Reflexive Property
• BE≅EB

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.9

CCSS.HSG.SRT.B.5

Claim: CS ≌ WD

Context: CW and SD bisect each other

Evidence: ​ CP≅PW by bisector

SP ≌ PD by​ (a)   ​ (b)   by​ (c)  

Explanation: ⊿CPS ≅ ⊿WPD by​ (d)   so CS ≌ WD​ (e)  

• bisector
• ∠CPS ≅∠DPW
• Vertical Angle
• SAS
• ≅ parts of ≅⊿
• ∠P ≌ ∠W
• Alt. Interior
• AAS
• SSS
• ASA

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

Claim: ⊿BCA≌⊿DAC

Context: ABCD is a Rhombus

Evidence: ​ (a)   property of Rhombus

AD≅BC property of Rhombus

​ ​ (b)   by Reflexive Property

Explanation:⊿BCA≌⊿DAC by​ (c)  

• AB≅DC
• AC≅AC
• SSS
• SAS
• ∠A≅∠C
• ASA
• AAS

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.11

CCSS.HSG.SRT.B.5

Claim: ⊿MAE≅⊿THE

Context: MATH is a Rhombus

Evidence: ​ AM ∥ MT​ (a)  

​ (b)   by property of Rhombus

​ (c)   by alt. interior angle

​ (d)   by vertical angle

Explanation: ⊿MAE≅⊿THE by​ (e)  

• property of a Rhombus
• AM≅MT
• ∠MAE ≅ ∠TME
• ∠AEM ≅ ∠HET
• AAS
• ASA
• SAS
• AE≅EH

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

CCSS.HSG.CO.C.11

CCSS.HSG.SRT.B.5