Given
:
⃗
AB
bisects
∠
DAB
∧
⃗
BA
bisects
∠
DCB
Prove
:
△
DAC
≅
△
BAC
Statements
Reasons
1.
⃗
AB
bisects
∠
DAB
2.
∠
DAC
≅
∠
BAC
3.
∠
AC
≅
∠
AC
4.
⃗
BA
bisects
∠
DCB
5.
∠
DCA
≅
∠
BCA
6.
△
DAC
≅
△
BAC
1. given
2. given
3. reflective
4. given
5. definition of vertical angles
6. prove
o
Is
△
XWY
≅
△
ZWY
by HL? YES
2.
NO
o
If yes, name the Legs that allow the use of HL.
If no, explain why not.
Yes they are equal since it equals 90 degrees.
1.
XY=ZY (Hypotenuse)
2.
YW is the common edge. (leg)
3.
Write a paragraph proof.
Given:
´
GH
≅
´
JH
and
´
FH
≅
´
HI
Prove:
´
FG
≅
´
JI
C
D
B
A
X
Y
W
Z
G
I
H
F
J

4.
Using the words from the word list, name all the parts of the isosceles triangle in the
diagram
below. Some words may be used more than once.
A._____
_base angle B. _____leg___________ C._____vertex_________
D._______leg________ E.______base angle __ F. _____base___________
5.
Which criteria for triangle congruence can be used to prove the pair of triangles below are
congruent? Explain.
SAA
AAS
SSS
AAA
SAS
ASA
All of the above except for AAA. The shape above looks like a rectangle so all the criteria for
congruence can be proven. AAA on its own is able to prove similarity but not congruence.
3. In the diagram, GH is equal to JH and FH is equal to HI. In this paragraph I am going to prove how FG equals JI.
First off, H is the midpoint for both triangles so that explains all the given points. The answer for FG=JI would be SSS.
It would be SSS because all three sides in the one triangle are congruent to the corresponding sides in the other.
WORD LIST:
Vertex
Leg
Base Angle
Base
C
D
B
F
A
E

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- Winter '16
- Mrs. Goodwin