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Name:________________________________________________
Date:________ Period:_______
Congruent Triangles Review: ANSWER KEY
Ms. Anderle
Congruent Triangles: Review ANSWER KEY
1. HL, ASA, AAS, SAS, SSS
2. Statement
1) SY||UD
2) <S <D; <U <Y
3) SD bisects YU
4) YT TU
**5)<STY & <UTD are
vertical angles.
** 6) <STY <UTD
7) ∆STY
∆UTD
3. Statement
1)
Reasons___________________________________
1) Given
2) Parallel lines cut by a transversal form
congruent alternate interior angles.
3) Given
4) A bisectors divides a segment into two
congruent segments.
5) Intersecting lines form vertical angles.
6) Vertical angles are congruent
7) AAS / **ASA (can only use if you used steps 5&6)
Reasons___________________________________
1) Given
2)
2) Given
3) <CBD and <CBA are
right angles.
4)
3) Perpendicular lines form right angles.
5)
5) Reflexive Property
6) ∆CBD and ∆CBA are right
triangles.
7) ∆CBD ∆CBA
8) <CDB
<CAB
4. Statement
1) CD bisects <ACB
2) <ACD <BCD
4) All right angles are congruent.
6) A triangle with one right angles is
a right triangle.
7) HL
8) CPCTC
Reasons___________________________________
1) Given
2) A bisector divides an angle into two congruent angles.
3)
3) Given
4) <CDA and <CDB are
right angles.
5)
4) Perpendicular lines form right angles.
6)
6) Reflexive Property
5) All right angles are congruent.
7) ∆ADC
∆DBC
8)
7) ASA
8) CPCTC
5. Statement
1) <ECB <ECD
Reasons___________________________________
1) Given
2) <ECB & <BCA are supplementary
<ECD & <DCA are supplementary
3) <BCA <DCA
2) Angles that form a linear pair are supplementary.
4) BC
CD
4) Given
5) AC
AC
5) Reflexive
6) ∆ABC
∆ADC
3) Supplements of congruent angles are congruent.
6) SAS
6. Statement
1) <1 <2
Reasons___________________________________
1) Given
2) <3
2) Given
<4
3) <3 & <CDA are supplementary
<4 & <CBA are supplementary
4) <CDA <CBA
3) Angles that form a linear pair are supplementary.
5) AC
5) Reflexive Property
AC
6) ∆ACD
7) DC
∆ABC
AB
4) Supplements of congruent angles are congruent.
6) AAS
7) CPCTC
7. Statement
1) <E <B
Reasons___________________________________
1) Given
2) DC
FA
2) Given
3) FC
FC
3) Reflexive
4) DC + FC
5) DF
FA + FC
AC
4) Addition Postulate
5) Substitution
6)
6) Given
7)
7) Given
8) <EDA & <CAB are right angles
9) <EDA <CAB
8) Perpendicular lines meet to form right angles.
9) All right angles are congruent.
10) ∆EDF
10) AAS
11) CB
∆ACB
EF
11) CPCTC
8. Statement
1) CA||BD
2) <CAE <EBD
Reasons___________________________________
1) Given
2) Parallel lines cut by a transversal form congruent
3) <ACE
alternate interior angles.
3) Parallel lines cut by a transversal form congruent
<EDB
4) E is the midpoint of CD
5) CE DE
alternate interior angles.
4) Given
5) A midpoint divides a segment into two congruent segments.
6) ΔCAE
6) AAS
ΔBED
7) CA
BD
7) CPCTC
***You can also prove <CEA and <BED by using vertical angles. If you use this method, you may be able
to prove the triangles congruent using ASA.***
9. Statement
1) DA EA
Reasons___________________________________
1) Given
2) A is the midpoint of GF
3)
2) Given
3) Given
4)
4) Given
5) <DGA and <EFA are right angles
6) <DGA <EFA
5) Perpendicular lines meet to form right angles.
6) All right angles are congruent.
7) ΔDGA and ΔEFA are right triangles. 7) A right triangle has one right angle.
8) ΔDGA ΔEFA
8) HL
9) DG
EF
9) CPCTC
10. Statement
1) ΔPQR is isosceles with base PR
2) PQ RQ
Reasons___________________________________
1) Given
2) An isosceles triangle has two congruent sides.
3) PS
SR
3) Given
4) SQ
SQ
4) Reflexive
5) ΔPSQ
11. SKIP
ΔRSQ
5) SSS
12. Statement
1) <1 <2
Reasons___________________________________
1) Given
2) <1 & <UEQ are supplementary
<2 & <AJC are supplementary
3) <UEQ <AJC
2) Angles that form a linear pair are supplementary
4) JQ
EC
4) Given
5) CQ
CQ
5) Reflexive
6) JQ – CQ
7) JC
EC – CQ
QE
8) JA
9) ΔJAC
10) AC
3) Supplements of congruent angles are congruent
6) Subtraction
7) Substitution
8) Given
ΔQUE
QU
9) SAS
10) CPCTC