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)  

​ Claim: ⊿ABC≌⊿ECD

Context:​ (a)   ​, ​​ (b)  

Evidence:​ (c)   by​ (d)  

Explanation: ⊿ABC≌⊿ECD BY​ (e)  

Claim:⊿WXZ≅⊿YZX

Context: WX∥YZ, ​ (a)  

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

Explanation: ⊿WXZ≅⊿YZX by​ (e)  

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 ⊿

Claim: ⊿ABE≅⊿CDE

Context: AB∥CD AE≅CE

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

Explanation: ⊿ABE≅⊿CDE by ​ (d)  

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)  

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)  

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)