1. Given: E and F are parallel planes, E contains AB, F contains CD, AC 1 F, and BD 1 F. Prove: AD and BC bisect each other. D

Linear Algebra: A Modern Introduction
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Chapter2: Systems Of Linear Equations
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Problem Set 10-1
1. Given: E and F are parallel planes, E
contains AB, F contains CD,
AC1 F, and BD 1 F.
Prove: AD and BC bisect each other.
2. If Kand Mare planes, K1 L at P, and
plane M1 L at T, what can you con-
clude about K and M? Why?
3. Prove the following statement true or false.
If E and F are parallel planes and E contains line L1 and F contains
line L2, then L1 || L2.
• B
G
4. Plane G contains points A, B, C, and
plane H contains points D, E, F such
that AD 1 G, AD 1 H, and AB =
DF. Which of the following state-
A
• C
•E
H
D
• F
ments must be true?
(b) BC || EF.
(e) AC 1 AD.
(c) AABC ADFE.
(f). LAFD ZDBA.
(h) AC || DF.
(a) AF = BD.
(d) G || H.
(g) AF and BD bisect each other.
5. In the figure, ABCD, ADEK, anc
OBCEK are parallelograms. Prove that
(a) EK || AD || BC, and
(b) ZKAB ZEDC.
K.
Transcribed Image Text:Problem Set 10-1 1. Given: E and F are parallel planes, E contains AB, F contains CD, AC1 F, and BD 1 F. Prove: AD and BC bisect each other. 2. If Kand Mare planes, K1 L at P, and plane M1 L at T, what can you con- clude about K and M? Why? 3. Prove the following statement true or false. If E and F are parallel planes and E contains line L1 and F contains line L2, then L1 || L2. • B G 4. Plane G contains points A, B, C, and plane H contains points D, E, F such that AD 1 G, AD 1 H, and AB = DF. Which of the following state- A • C •E H D • F ments must be true? (b) BC || EF. (e) AC 1 AD. (c) AABC ADFE. (f). LAFD ZDBA. (h) AC || DF. (a) AF = BD. (d) G || H. (g) AF and BD bisect each other. 5. In the figure, ABCD, ADEK, anc OBCEK are parallelograms. Prove that (a) EK || AD || BC, and (b) ZKAB ZEDC. K.
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