Agenda:
1. Check HW
2. QUIZ(4.1-4.5) - TUESDAY
3. WS(4.1-4.5) - complete through Proof #4 by Monday (we will complete the
remaining proofs in class on Monday)
4. ALEKS 9 (8 topics) due TONIGHT (minimum total = 69 topics)
HW:
(HR): (4.5)Pg.279: 7, 9, 11, 17, 19
Obj: To prove triangles congruent by ASA and AAS.
Study Guide (4.1-4.5)
* Given the vertices of a triangle, classify it by its sides and angles.
* Complete the proof of the Triangle Sum Theorem
* Find missing angle measures of triangles in a diagram. (apply the Triangle Sum Theorem,
Exterior Angle Theorem, Isosceles Triangle Theorem)
* Write 2-Column proofs involving proving triangles congruent. (SSS, SAS, ASA, AAS, HL, and
CPCTC)
Geometry
Keckler
Worksheet (4.1-4.5)
Name: ______________________
Per: ____
Date: ________
1. Classify the triangle by its sides and angles. (Show work)
A(-6,1), B(0,-4), C(8,3)
2. Complete the proof of the Triangle Sum Theorem by filling in the missing reasons.
Given:
A
4 2 5
ABC
D
Prove: m 1 + m 2 + m 3 = 180o
B
1
3
C
Statements
Reasons
1.
1. _________________________
ABC
2. Draw AD through A parallel to BC.
2. _________________________
3.
4 and
BAD form a linear pair.
3. _________________________
4.
4 and
BAD are supplementary.
4. _________________________
5.
m 4+m
6.
m
7.
m 4+m 2+m
8.
9.
BAD = 180o
5. _________________________
BAD = m 2 + m 5
6. _________________________
4=
1;
m 4= m
5 = 180o
5 =
1;
3
m 5=m 3
10. m 1 + m 2 + m 3 = 180o
7. _________________________
8. _________________________
9. _________________________
10. _________________________
4. Find the measure of each numbered angle.
3. Find the value of x.
(2x-11)
(2x+27)
o
4
m 1 = ____
6
m 2 = ____
o
100
o
1 2
3
5
m 3 = ____
m 4 = ____
m 5 = ____
m 6 = ____
x = _______
5. Find the measure of each numbered angle.
m 1 = ____
m 2 = ____
m 3 = ____
m 4 = ____
m 5 = ____
m 6 = ____
Sections (4.4-4.5)
Geometry
Name: _______________________
Write two-column proofs.
D
A
1. Given: AD = CB
AD ll CB
Prove:
ABC =
Statement
CDA
B
C
Reason
N
2. Given: PN bis.
MNO
MN = ON
Prove:
MNP =
ONP
M
Statement
3. Given:
1=
6
Reason
A
D
BC = EC
2
1
B
Prove: AC = DC
3 4
C 5
6
E
G
F
Statement
O
P
Reason
B
4. Given: C bis. AE
AB ll CD
A
D
C
AB = CD
Prove:
D=
B
E
Statement
5. Given: AC
Prove:
A
bis. BD
ABC =
Reason
ADC
B
Statement
C
Reason
D
A
6. Given: AB ll CD
B
AC ll BD
Prove:
ABC =
DCB
C
D
Statement
Reason
Z
7. Given: WU ll YV
Y
X
W
XU ll ZV
WX = YZ
Prove:
WXU =
YZV
Statement
V
Reason
U
8. Given:
ABC and
ABD are standing on plane P
A
AB BC
AB BD
AC = AD
Prove:
B
ABC =
ABD
P
Statement
Reason
9. Given: A(-4,2), B(-3,-3), C(-1,0), D(4,1), E(1,3)
Prove:
ABC=
CDE
C
D