ProvingTheoremsusingTriangleProofs
Definitionofaparallelogram:Aquadrilateralwherebothpairsofoppositesidesareparallel
Given: Figure ABCD is a parallelogram
A
B
E
D
C
Statement
1.)
Provethataparallelogram’s
oppositesidesmustalsobecongruent
Prove: AB ≅ CD, and AD ≅ BC
2.)
Provethataparallelogram’sdiagonals Statement
bisectoneanother
Prove: AE ≅ CE, and DE ≅ BE
Definitionofarectangle:Aparallelogramthatalsohas4congruentrightangles
3.)
Provethatarectangle’sdiagonals
willbecongruent
Given: Figure ABCD is a rectangle
A
B
E
D
C
Prove: AC ≅ BD
Statement
Reason
Reason
Reason
Definitionofarhombus:Aparallelogramthatalsohas4congruentsides
Given: Figure ABCD is a rhombus
A
B
E
D
C
4.)
Provethatarhombus’diagonalsare
perpendicular
Prove: AC ⊥ BD
5.)
Provethatarhombus’diagonalsbisect
theanglesoftherhombus
Prove: AC bisects ∠BAD and ∠BCD,
BD bisects ∠ABC and ∠ADC
Statement
Reason
Statement
Reason
DefinitionofMidsegment:Alinesegmentthatpassesbetweentwomidpointsofatriangle
6.)
Provethatthemidsegmentisparallel
tothethirdsideofthetriangle
Given:
DE is a midsegment of ABC
Prove: DE BC
A
E
D
C
B
Statement
Reason
7.)
8.)
Statement
Provethisaboutthemedian
Reason
Given: BD is a median of ABC, and
ABC is isosceles
B
A
D
C
Prove: BD is also a perpendicular
bisector of AC
ProvetheIntersectingChordsTheorem
Given: AB and CD be chords of
intersect at point E
Statement
Reason
O and
C
A
E
Let: AE = a
BE = b
CE = c
DE = d
O
D
B
Prove: ab = cd
S
9.)
Given: ∠OPQ ≅ ∠SRQ
R
Q
P
PQ OQ
Prove:
=
QR QS
O
Statement
Reason
Statement
10.) T
11.) A
12.) Reason
Given: TV = 4, UV = 8, UX = 6
UV is the perpendicular bisector of TW
U
X
W
V
Prove: ∠TUV ≅ ∠XWV
B
Statement
Given: ∠BAD ≅ ∠BCD
BD bisects ∠ABC
D
Reason
C
Prove: AB ≅ CB
Statement
Reason