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Geometry
Triangle Congruence Proofs – Congruent Right Triangles – HL Theorem
What additional information would you need to prove the triangles congruent by the HL Theorem?
1) ∆ABC ≅ ∆XYZ
2) ∆ABC ≅ ∆DCB
Z
A
X
A
B
C
D
Y
B
C
3) ∆STR ≅ ∆PQ
S
4) ∆ACT ≅ ∆GCV
T
C
A
R
Q
G
P
T
V
Write a two Column Proof.
5)
Given: WJ ≅ KX , ∠JWX and ∠XKJ are right angles
W
X
J
K
Prove: ∆WJX ≅ ∆KJX
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Given: EB ≅ DB, ∠A and ∠C are right angles
6)
E
D
B is the midpoint of AC
Prove: ∆BEA ≅ ∆BDC
A
7)
B
C
C
Given: CD ≅ EA, AD is the perpendicular bisector of CE
Prove: ∆CBD ≅ ∆EBA
A
B
E
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D
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Answer Key
1) ∠C and ∠Z are right angles
2)
AC ≅ BD or AB ≅ CD
3) RT ≅ Q
4) ∠ATC and ∠GVC are right angles
∠JWX and ∠XKL are right ∠s .......... Given
∆JWX and ∆XKL are right ∆s .......... Definition of right ∆
5)
JX ≅ JX .......... Reflexive Property
WJ ≅ KX .......... Given
∆WJX ≅ ∆KXJ .......... HL Theorem
∠A and ∠C are right ∠s .......... Given
∆BEA and ∆BDC are right ∆s .......... Definition of right ∆
6)
B is the midpoint of AC .......... Given
AB ≅ CB .......... Definition of Midpoint
EB ≅ DB .......... Given
∆BEA ≅ ∆BDC.......... HL Theorem
AD is the ⊥ of CE .......... Given
∠CBD and ∠EBA are right ∠s .......... Definition of ⊥ lines
B is the midpoint of CE.......... Definition of bisector
7) ∆CBD and ∆EBA are right ∆s .......... Definition of right ∆
CB ≅ EB .......... Definition of Midpoint
CD ≅ EA .......... Given
∆CBD ≅ ∆EBA.......... HL Theorem
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