Name: ____________________________________________________
Day 36: Congruence Criteria for Triangles Review Day 1
Date: __________
CC Geo M1TD
1.List the 5 ways of proving triangles congruent:
1.
2.
3.
4.
5.
2.What two sets of criteria CANNOT be used to prove triangles congruent:
1.
2.
3.In the diagram at the right BC  AD, ED  AD, AF  CD, A  EFD .
Which method proves that ACB  FDE ?
(1)ASA (Angle-Side-Angle)
(2) AA (Angle-Angle)
(3) SAS (Side-Angle-Side)
(4) HL (Hypotenuse-Leg)
4. The figure to the right shows the construction of an angle bisector. B and C are
each connected to D. The construction marks can be used to prove DABD is
congruent to DACD . Given a rigid motion that would reflect DABD in AD , such
that the point B maps to point C and the radii in the arcs are congruent, these
triangles could be proven congruent by
(1)SAS only
(2) SSS only
(3) SSS or SAS
(4) ASA or HL
In 5-6, mark the appropriate congruence markings to use the method of proving that is stated:
5. SAS
6. AAS
1
7. In ABC and XYZ , C  Z and BC  YZ . Write one additional statement that could be used to prove that
the two triangles are congruent. State the method that would be used to prove that the triangles are congruent.
8. Given m || n . Determine whether triangle ABC is congruent to triangle DEF. Justify your response.
---------------------------------------------------------------------------------------------------------------------------------------------------------------Prove the following using any method of triangle congruence that we have discussed.
9. Given: AE  DB, CF  DB, DE  FB, DC  AB
Prove:
ABE @ CDF
Precisely describe a single rigid motion that maps CFD onto AEB .
2
10. Given: 1  2 , AC bisects BAD
Prove: AD  AB
Describe the rigid motion(s) that maps one congruent triangle to the other.
11. Given: DE  GE , DE  BC , GE  BA
Prove: DBE  GBE
Describe the rigid motion(s) that maps one congruent triangle to the other.
3
DOUBLE TRIANGLE CONGRUENCE FILL IN PROOF
12. Given: ME  SE , MH  SH
Prove: MKH  SFH and KH  FH
Statements
1.
ME  SE
Reasons
1. Given
MH  SH
2.
2. Reflexive Property
3. MEH  SEH
3.
4. M  S
4.
5.
5. Vertical angles are congruent
6. MKH  SFH
6.
7. KH  FH
7.
4