Question 1
Question: 
Answer: Data:
AB = BC and AD = CE
To prove:
AD = CE
Proof:
AB=BC (data)
AD=CE (data)
BD=BE (If equals are subtracted from equals, the remainders are also equal)
In D AEB and D CDB,
AB=BC (data)
BE=BD (proved above)
(common angle to both the triangles)
Question 2
Question: ABC and DEF are two triangles such that AB = DE, 
Answer: Data:
AB=BC and AD=CE
To prove:
Proof:
Comparing triangles ABC and DEF,
AB=DE (data)
BC = EF (data)
Question 3
Question: 
Answer: Data:
To prove:
Proof:
Comparing D GCB and D DCE,
BC=CE (data)
Question 4
Question: ABC and ABD are two triangles such that AD=BC, BD=AC.
Answer: Data:
In triangles ABC and ABD, AD=BC and BD=AC.
To prove:
Proof:
Comparing D ABC and D ABD ,
BC = AD (data)
AC = BD (data)
AB = AB (common side to both triangles)
Question 5
Question: 
Answer: Data:
AB = DE
To prove:
Proof:
BF = DG (corresponding sides)
In D ABF and D DGE,
(data)
AB = DE (data)
BF = DG (from above)
Question 6
Question: 
Answer: Data:
GE = FA
To prove:
AB = DE
Proof:
(data)
BF = DG (corresponding sides of congruent triangles)
(supplements of equal angles are equal)
In D ABF and D DGE,
BF = DG (prove above)
AF = GE (data)
\ AB = DE (corresponding sides)
Question 7
Question: 
Answer: Data:
GH = FH
To prove:
BG = DF
Proof:
BC = CD
BF = GD (corresponding sides of congruent triangles)
(corresponding angles of congruent triangles)
Compare D GBH and D DHF,
GH = FH (data)
BF+FH = GD+GH (BF=GD and FH=GH)
i.e., BH = DH
(proved above)
BG = DF (congruent parts of congruent triangles)
Question 8
Question: 
Answer: Data:
QR = SR
To prove:
Proof:
Compare D TQR and D TSR,
QR = SR (data)
TR = TR (common side)
QT = TS (CPCT)
Now compare D PTQ and D PTS,
TQ = TS (prove above)
PT = PT (common side)
Question 9
Question: 
Answer: Data:
To prove:
CF=BE
Proof:
Comparing D FAC and D BED,
(data)
(data)
AC = BD (AB=CD given. Add BC to both sides. We get
AB+BC = CD+BC
i.e., AC=BD)
CF=BE ( CPCT)
Question 10
Question: In the following examples, the hypothesis is marked on the diagram. Write the postulate of congruence you would use to support your argument that the triangles are congruent. If more than one hypothesis is applicable to any example, state both.
Answer: i)
Postulate : SAS
ii)
Postulate : SSS, SAS
iii)
Postulate : ASA
iv)
Postulate : SSS
v)
Postulate : SAS
