Download Lesson 4.7 • Flowchart Thinking

Lesson 4.7 • Flowchart Thinking
Name
Period
Date
Complete or write a flowchart for each proof.
SR
and PQ
SR
1. Given: PQ
S
R
QR
Show: SP
P
Flowchart Proof
Q
Given
PQ SR
__________________
__________________
PQS ______
SP QR
_________________
__________________
QS ______
__________________
KI
2. Given: Kite KITE with KE
I
bisects EKI and ETI
Show: KT
K
Flowchart Proof
T
E
KE KI
ETK ITK
______________
_______________
__________________
KET ______
KITE is a kite
______________
________________
Definition
of bisect
__________________
______________
3. Given: ABCD is a parallelogram
Show: A C
D
A
C
B
Flowchart Proof
AB CD
ABCD is a parallelogram
_____________
Definition of
___________
_________________________
Same segment
____________
_____________
______________
_____________
Discovering Geometry Practice Your Skills
©2003 Key Curriculum Press
CHAPTER 4
29
9. ABE DEB (ASA or SAA); DEB BCD
(ASA or SAA); ABE BCD (Both are
congruent to DEB.)
8 and
10. Q(18, 9), R(20, 7). Slope BC
slope QR 8. They have the same slope
so they are parallel.
CF
(see Exercise 10).
11. Possible answer: DE
DEF CFE because both are right angles,
FE
because they are the same segments. So,
EF
FD
by CPCTC.
DEF CFE by SAS. EC
12. Possible answer: Because TP RA and
RT
,
PTR ART are given and TR
being the same segment, PTR ART
RP
by CPCTC.
by SAS and TA
LESSON 4.6 • Corresponding Parts of Congruent
Triangles
LESSON 4.7 • Flowchart Thinking
1. SSS, SAS, ASA, SAA
1. (See flowchart proof at bottom of page.)
2. Third Angle Conjecture (or CPCTC after SAA)
2. (See flowchart proof at bottom of page.)
and QR
are
3. Triangles are congruent by SAA. BC
corresponding parts of congruent triangles.
4. AIA Conjecture
5. AIA Conjecture
6. ASA
7. CPCTC
3. (See flowchart proof at bottom of page.)
LESSON 4.8 • Proving Isosceles Triangle Conjectures
1. AD 8
2. mACD 36°
1
3. mB 71°, CB 192 4. mE 60°
5. AN 17
6. Perimeter ABCD 104
ZX
by CPCTC.
8. YWM ZXM by SAS. YW
BD
by CPCTC.
9. ACD BCD by SAS. AD
10. Possible answer: DE and CF are both the distance
and AB
. Because the lines are parallel,
between DC
CF
.
the distances are equal. So, DE
Lesson 4.7, Exercises 1, 2, 3
1.
PQ SR
Given
PQ SR
PQS RSQ
PQS RSQ
SP QR
Given
AIA Conjecture
SAS Conjecture
CPCTC
QS QS
Same segment
2.
KE KI
Given
ETK ITK
KITE is a kite
TE TI
KET KIT
CPCTC
KT bisects EKI
and ETI
Given
Definition of
kite
SSS Conjecture
EKT IKT
Definition of
bisect
CPCTC
KT KT
Same segment
3.
ABD CDB
AB CD
ABCD is a parallelogram
Definition of
parallelogram
Given
AIA Conjecture
BD DB
BDA DBC
A C
Same segment
ASA Conjecture
CPCTC
AD CB
Definition of
parallelogram
Discovering Geometry Practice Your Skills
©2003 Key Curriculum Press
ADB CBD
AIA Conjecture
ANSWERS
97
7. (See flowchart proof at bottom of page.)
6. 170°; 36 sides
7. 15 sides
8. Given: Isosceles ABC
BC
and
with AC
median CD
bisects ACB
Show: CD
8. x 105°
9. x 105°
Flowchart Proof
C
10. x 18°
11. mHFD 147°
LESSON 5.2 • Exterior Angles of a Polygon
A
D
B
CD is a median
Given
AC BC
AD BD
CD CD
Given
Definition of
median
Same segment
ADC BDC
2
1. a 64°, b 1383°
2. a 102°, b 9°
3. a 156°, b 132°, c 108°
4. 12 sides
5. 24 sides
6. 4 sides
7. 6 sides
8. mTXS 30°, mSXP 18°, mPXH 12°,
mHXO 15°, mOXY 45°
9. Each exterior angle is cut in half.
SSS Conjecture
10. a 135°, b 40°, c 105°, d 135°
ACD BCD
11.
CPCTC
CD bisects
ACB
Definition of
bisect
12.
LESSON 5.1 • Polygon Sum Conjecture
1. a 103°, b 103°, c 97°, d 83°, e 154°
108°
108°
108°
2. x 121.7°, y 130°
3. p 172°, q 116°, r 137°, s 90°, t 135°
4. a 92°, b 44°, c 51°, d 85°, e 44°,
f 136°
5. mE 150°
3. x 64°, y 43°
70° D
A
LESSON 5.3 • Kite and Trapezoid Properties
2. x 124°, y 56°
110°
125°
85°
108°
1. x 30
C
B
108°
4. x 12°, y 49°
150°
E
Lesson 4.8, Exercise 7
CD CD
Same segment
CD is an altitude
Given
98
ADC and BDC
are right angles
Definition of altitude
ANSWERS
ADC BDC
ADC BDC
AD BD
CD is a median
Both are right angles
SAA Conjecture
CPCTC
Definition of
median
AC BC
A B
Given
Converse of IT
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©2003 Key Curriculum Press