Download 5.2-5.4, 6.2 - rosenmath.com

Warm Up
90 + 30 + m<L = 180
120 + m<L = 180
m<L = 60
7z + 6 = 90
7z= 84
z = 12
1.
4.
12
24
LN = 2(18) – 12
LN = 24
5y = 90
y = 18
2.
5.
18
60o
m<C = m<L
m<C = 60
3.
60o
6.
24
AC = 12 + 12
AC = 24
(also, AC = LN)
Marking Congruent Triangles
Thm. Corresponding Parts of Congruent
Triangles are Congruent (CPCTC)
If two triangles are congruent, then their
corresponding parts are congruent.
Angle-Side-Angle (ASA)
If two angles and the ______________
included
side of one
congruent
triangle are _____________
to two angles and the
____________
side of a second triangle, then the
included
congruent
two triangles are ________________.
Side-Angle-Side (SAS)
If two sides and the _____________
included
angle of one
triangle are __________
congruent to two sides and the
included angle of a second triangle, then the two
triangles are ____________
congruent
Side-Side-Side (SSS)
congruent to
If 3 sides of one triangle are _____________
three sides of a second triangle, then the two
congruent
triangles are ________________.
Angle-Angle-Side (AAS)
E
A
F
B
C
D
nonincluded
If two angles and a _____________________
side of one
congruent to two angles and the
triangle are _______________
nonincluded
corresponding ____________________
side of a second
congruent
triangle, then the two triangles are ________________.
Hypotenuse-Leg (HL)
If the hypotenuse and a leg of a right triangle
are congruent to the hypotenuse and leg of a
second right triangle, then the two triangles are
congruent .
Does AAA work?
Does AAA work?
NO!
Does ASS work?
No!
There is no ASS in geometry!
Very Important
Other that the “given” information, you can only
mark three things.
1.Shared Side (Overlapping Side)
or a Shared Angle
2. Vertical Angles
3. Alternate Interior Angles (only if lines parallel).
Shared Side
D
A
B
statement
C
reason
Vertical Angles
statement
reason
Alternate Interior Angles (only if lines parallel)
E
statement
B
C
D
A
reason
Decide whether the triangles are congruent. Explain
your reasoning.
Yes, SAS
Decide whether the triangles are congruent. Explain your reasoning.
Yes, AAS
Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
Decide whether the triangles are congruent. Explain your reasoning.
No,
SSA doesn’t work!
Decide whether the triangles are congruent. Explain your reasoning.
Yes, AAS
Ex. State the third congruence that must be given to prove
ABC  DEF.
GIVEN: AC  DF , A  D, ____________
Use the AAS Congruence Theorem.