### Slide 1

```8. BC = ED = 4; BC = EC = 3; DC = DC by Reflex so ΔBCD  ΔEDC by SSS
9. KJ = LJ; GK = GL; GJ = GJ by Reflex so ΔGJK  ΔGJL by SSS
12. YZ = 24, ST = 20, SU = 22 so XY = ST, YZ = TU, XZ = SU so ΔXYZ  ΔSTU by SSS
13. Given
DB = CB
AB  DC
Def of 
Rt   Thm
AB = AB
SAS
14. SAS
15. SAS
16. Neither
17. Neither
18. To use SSS, need AB = DE and CB = CE
To use SAS, need CB = CE
20. AB = √17, BC = 5, AC = √26, DE = √17, EF = 5, DF = 4, Δs not 
21. Given
Def of 
mWVY  mZYV
Def of 
Given
VY = VY
SAS
23. Check drawings ex. 7-7-1 and 6-6-3
24. X = 5.5, AB = BD, BC = DC (def of ), AC = AC (reflex), so ΔABC  ΔADC by SSS
42. 86
43. 34°
44. 70°
Warm Up
1. What are sides AC and BC called? Side
AB?
legs; hypotenuse
2. Which side is in between A and C?
AC
3. Given DEF and GHI, if D  G and
E  H, why is F  I?
Third s Thm.
An included side is the common side of two consecutive
angles in a polygon. The following postulate uses the
idea of an included side.
Example 2A:
Determine if you can use ASA to prove the
triangles congruent. Explain.
Two congruent angle pairs are give, but the included
sides are not given as congruent. Therefore ASA
cannot be used to prove the triangles congruent.
Example 2B:
Determine if you can use ASA to
prove NKL  LMN. Explain.
By the Alternate Interior Angles Theorem. KLN  MNL.
NL  LN by the Reflexive Property. No other congruence
relationships can be determined, so ASA cannot be
applied.
You can use the Third Angles Theorem to prove
another congruence relationship based on ASA. This
theorem is Angle-Angle-Side (AAS).
AAS using only steps 1 and 3
Example 3:
Use AAS to prove the triangles congruent.
Given: X  V, YZW  YWZ, XY  VY
Prove:  XYZ  VYW
Statements
Reasons
1.
X  V
1.
Given
2.
YZW  YWZ
2.
Given
3.
XY  VY
3.
4.
 XYZ  VYW
4.
Given
AAS
Example 4A:
Determine if you can use the HL Congruence Theorem to
prove the triangles congruent. If not, tell what else you
need to know.
According to the diagram, the triangles
are right triangles that share one leg.
It is given that the hypotenuses are
congruent, therefore the triangles are
congruent by HL.
This conclusion cannot be proved by HL.
According to the diagram, the triangles
are right triangles and one pair of legs is
congruent. You do not know that one
hypotenuse is congruent to the other.
Example 4
Determine if you can use
the HL Congruence Theorem
to prove ABC  DCB. If
not, tell what else you need
to know.
Yes; it is given that AC  DB. BC  CB by the
Reflexive Property of Congruence. Since ABC
and DCB are right angles, ABC and DCB are
right triangles. ABC  DCB by HL.
```