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Geometry A
4.1 Angles of Triangles
1.
Name _______________________
Hour ______ Date ____________
ASSIGNMENT
Find m∠T.
2. Find the measures of the missing angles.
3. Find the measures of the numbered angles.
4. Find the measures of the numbered angles.
5. Find the measures of the numbered angles.
6. Find m∠1
7. Find x.
8. Find x.
Review:
9. Suppose 1 and 2 are vertical angles. If m1 = 4x + 2 and m2 = 8x – 14, find m2.
10. Suppose R is between Y and W. If RY = 3x – 10, RW = 66, and YW = 5x + 6, find RY.
1
Geometry A
4.2 Congruent Triangles
Name _________________________
Hour _______ Date ______________
ASSIGNMENT
1.
If RTY  KNB complete each pair of congruent parts:
_______  N
R  _______
RT  _______
Y  _______
_______  NB
RY  _______
Identify the congruent triangles in each diagram.
2.
3.
MNO  _________
SQP  _________
4.
5.
RVT  _________
EFD  _________
6. Using the diagram on the right, identify each pair of congruent parts:
R  _______
RT  _______
TVR  _______
T  _______
TV  _______
VR  _______
2
Review:
For #7-10, select the property, definition, postulate, or theorem from the box below that justifies each
statement. Write the property, definition, postulate, or theorem on the line provided.
reflexive property
symmetric property
transitive property
addition property
segment addition postulate
supplement theorem
subtraction property
multiplication property
division property
substitution property
angle addition postulate
distributive property
midpoint theorem
definition of an angle bisector
vertical angles theorem
complement theorem
7.
If m4 = m5, then m4 + 20 = m5 + 20
__________________________________
8.
AD = AD
__________________________________
9.
If AB  BC and BC  CE , then AB  CE
__________________________________
10.
If 3(x + 2) = 60, then 3x + 6 = 60
__________________________________
3
Geometry A
4.3 Proving Congruence
Name _________________________
Hour _______ Date ______________
ASSIGNMENT
For each problem, determine which postulate (SSS, SAS, AAS, ASA, or HL) can be used to prove th
triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
4
Identify whether each pair of triangle are congruent by SSS, SAS, ASA, AAS or HL. Otherwise, write
“not enough information.”
5
Geometry A
4.4 Triangle Congruence Proofs
Name _________________________
Hour _______ Date ______________
ASSIGNMENT
1. Given: RS  TS , V is the midpoint of RT
Prove: RSV  TSV
Statements
Reasons
1. RS  TS
1.
2.
2. Given
3.
3. Midpoint Theorem
4. VS  VS
4.
5. RSV  TSV
5.
2. Given: JK  MK , N  L
Prove: JKN  MKL
Statements
Reasons
1. JK  MK
1.
2. N  L
2.
3. JKN  MKL
3.
4. JKN  MKL
4.
6
3. Given: QR || TU , S is the midpoint of QT
Prove: RS  US
Statements
Reasons
1.
1. Given
2. Q  T
2.
3. S is the midpoint of QT
3.
4.
4. Midpoint Theorem
5.
5. Vertical Angles Theorem
6. QSR  TSU
6.
7. RS  US
4. Given: D  F , GE bisects DEF
Prove: DG  FG
Statements
Reasons
1. D  F
1.
2. GE bisects DEF
2.
3.
3. Definition of Angle Bisector
4.
4. Reflexive Property
5.
5.
6. DG  FG
6.
7
Geometry A
4.5 Isosceles and Equilateral Triangle Proofs
Name _________________________
Hour _______ Date ______________
ASSIGNMENT
1. Given: FE  HI
G is the midpoint of both EI and FH .
F
I
Prove: FEG  HIG
G
E
1. FE  HI
1.
2. G is the midpoint of both EI and FH .
2.
3.
3. Midpoint Theorem
4.
4. Midpoint Theorem
3. FEG  HIG
3.
2. Given: RQ // TS ; RQ  TS
H
R
S
Prove: QRT  STR
Q
1. RQ // TS
1.
2. RQ  TS
2.
3. QRT  STR
3.
4. RT  RT
4.
5. QRT  STR
5.
8
T
3. Given: L is the midpoint of WE ; WR // ED
R
E
L
Prove: WRL  EDL
W
D
1. L is the midpoint of WE
1.
2. WR // ED
2.
3.
3. Midpoint Theorem
4. RWL  DEL
4.
5. RLW  DLE
5.
6. WRL  EDL
6.
4. Given: MPR is isosceles with vertex P,
PN  MR
P
Prove: MN  NR
M
1. MPR is isosceles with vertex P
1.
2. PN  MR
2.
3. MP  RP
3.
4. PN  PN
4.
5. MPN  RPN
5.
6. MN  NR
6.
9
R
N
Review:
7.
Find the value of y in the figure at the right.
(3y + 12)o
Multiple Choice:
8.
Given: mA + mB = 150.
Conjecture: A and B are both acute angles.
Which one of the following is a counterexample to the conjecture?
A.
B.
C.
D.
9.
mA = 100 and mB = 50
mA = 45 and mB = 105
mA = 65 and mB = 85
None of the above statements is a counterexample because the conjecture is true.
Which one of the following pairs of slopes are slopes corresponding to perpendicular lines?
A.
9
2
and
3
6
B. 
12
3
and 
8
2
C. 
10
2
12
and
8
3
D.
10
3
and 
15
2
Geometry A
4.6 Constructing Triangles
Name _________________________
Hour _______ Date ______________
ASSIGNMENT
1. Construct a triangle that has the following 3 side lengths.
2. Construct a triangle that has the following 2 side lengths and included angle.
3. Construct a triangle that has the following angles and included side length.
4. Construct an equilateral triangle that has the following side length.
11
Review:
For #5 and 6, identify each pair of angles.
5.
 4 and  2
A. Alternate Interior Angles
B. Alternate Exterior Angles
C. Corresponding Angles
D. Consecutive Interior Angles
E. Vertical Angles
6.
 6 and  14
A. Alternate Interior Angles
B. Alternate Exterior Angles
C. Corresponding Angles
D. Consecutive Interior Angles
E. Vertical Angles
12
Geometry A
Unit 4 Review
Name _______________________
Hour _______ Date ___________
1. Find the measure of each indicated angle.
2. Find the measure of each indicated angle.
m1 = _________
m1 = _________
3. Find the measure of each indicated angle.
4. Find the measure of each indicated angle.
m1 = ______ m2 = _______ m3 = _______
m1 = ______ m2 = _______ m3 = _______
m2 = _________
5. Find the measure of each indicated angle.
m1 = _________
m2 = _________ m3 = _________ m4 = _________ m5 = _________
13
6.
Refer to the figure below.
Find the measure of each indicated angle if m6 = 51o and m8 = 134o.
m1 = _________
m2 = _________ m3 = _________ m4 = _________ m5 = _________
m7 = _________
m9 = _________ m10 = ________ m11 = ________ m12 = _________
7. Find the value of x, AB, BC, and AC if ABC
is equilateral.
x = __________
8. Find the value of x.
AB = _________
BC = ________
AC = _________
9. Suppose JKM is isosceles with vertex angle
K. If JK = 5x – 3, JM = 3x + 7, and KM = 2x + 9,
find the value of x, JK, JM, and KM.
x = __________
JK = _________
JM = ________
KM = _________
10. Suppose JKM is isosceles with vertex angle
K. If mJ = 8x – 5 and mM = 3x + 25, find
mK.
14
11. Suppose that FJ  FH and HF  HG .
If m  FHG = 126°, find m  J.
12. Suppose that AB  DB and CD  BD .
If m  A = 31°, find m  BDC.
F
J
A
mJ = _________
13.
C
D
G
H
B
mBDC = _________
Identify the congruent triangles in the figure below.
Then name the corresponding congruent angles and congruent sides for the congruent triangles.
FGD  ____________
14.
FGD  __________
DG  _________
GDF  __________
FD  _________
DFG  __________
FG  _________
Identify the congruent triangles in the figure below.
Then name the corresponding congruent angles and congruent sides for the congruent triangles.
MNO  ____________
NMO  __________
MN  _________
N  __________
OM  _________
NOM  __________
NO  _________
15
15.
Determine whether you can prove that each pair of triangles is congruent by using
SSS, SAS, ASA, AAS, or HL. If it is not possible to prove that the triangles are
congruent, write not possible.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
16
16.
Given: BD bisects ABC
AB  CB
Prove: BDA  BDC
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
17.
Given: A  C
ADB  CBD
Prove: ADB  CBD
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
18.
Given: P is the midpoint of NS
N  S
MPN  RPS
Prove: MN  RS
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
17
19.
Complete the following proof.
Given: AB || DE
AD bisects BE
Prove: AC  DC
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
20.
Complete the following proof.
Given: AE  CF
ABC is isosceles with
vertex angle B.
Prove: BE  BC
Statements
Reasons
1. AE  CF
1.
2. ABC is isosceles with vertex angle B.
2.
3.
3. Definition of an Isosceles Triangle
4. A  C
4.
5. ABE  CBF
5.
6.
6.
18
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