Question

https://static.k12.com/nextgen_media/assets/8074848-NG_GMT_A_02_U01_Quiz_DP024_102_001_prompt.jpg

Which lines are parallel in the square pyramid?

Select each correct answer.

A.​​​ BC←→ ​ and DE←→

B.​ AD←→ ​ and ​​ ​ BC←→ ​

C. AB←→ and AD←→

D. CD←→ and BE←→

Answer 1

@Vocaloid

Answer 2

Parallel=lines that never intersect

Answer 3

the arrows is on the top

Answer 4

any ideas? for example, just test the answer choices one by one: are BC and DE parallel? check the original picture

Answer 5

yes

Answer 6

good, so A is one possibility

what about choice B? are AD and BC parallel?

Answer 7

no

Answer 8

good, so eliminate B

what about choice C? are AB and AD parallel?

Answer 9

no

Answer 10

good, what about choice D? are CD and BE parallel?

Answer 11

yes

Answer 12

good so A&D are your solutions

Answer 13

https://static.k12.com/nextgen_media/assets/1541442-IM1_141006_050213.jpg

The figure shown is a rectangular prism.

Which edges are parallel to AH¯¯¯¯¯¯ ?



Select each correct answer.


A. PA¯¯¯¯¯

B. BD¯¯¯¯¯

C. DK¯¯¯¯¯¯

D. BM¯¯¯¯¯¯

E. MK¯¯¯¯¯¯¯

Answer 14

the lines are on top

Answer 15

well let's try drawing them out

Answer 16

all the lines parallel to AH are marked in red - which choices correspond?

Answer 17

BD, PA, MK

Answer 18

hm not quite, PA is this side so it's not parallel

but BD + MK = your solutions

Answer 19

BD and MK are my only solutions

Answer 20

yup the others are perpendicular

Answer 21

https://static.k12.com/nextgen_media/assets/1541443-IM1_141006_050214.jpg

The figure shown is a rectangular prism.

Which edges are perpendicular to PR¯¯¯¯¯ ?



Select each correct answer.


A. QT¯¯¯¯¯

B. TJ¯¯¯¯¯

C. HP¯¯¯¯¯¯

D. TR¯¯¯¯¯

E. RA¯¯¯¯¯

Answer 22

similar logic as last time but we want all the perpendicular edges

Answer 23

actually I missed one, include TR

Answer 24

QT, HP, TR

Answer 25

hm not quite, QT is parallel not perpendicular

Answer 26

notice how RA is also perpendicular to PR
so it's every choice except QT

Answer 27

https://static.k12.com/nextgen_media/assets/1541446-IM1_141006_050217.jpg

Rodrigo knows that AM←→−⊥MN←→− and UK←→⊥MN←→− .

What other facts can Rodrigo conclude are true?



Select each correct answer.


A. AL←→∥UK←→

B. AL←→⊥LT←→

C. MN←→−∥LT←→

D. m∠MBK = 90°

Answer 28

by the way with the other question it's every choice but that doesn't include QT ?

Answer 29

yes

Answer 30

well let's go one by one

AM is perp. to MN
UK is perp. to MN

there's a theorem that states: if two lines (let's call them A and B) are both perpendicular to the same line (let's call it C) then A + B are parallel making statement 1 true

Answer 31

however we don't know anything about LT (it "looks" perpendicular but there's no evidence such as angle measurements or markings to show that LT is parallel to anything) eliminating choices B +C

Answer 32

as for choice D: <MBK is the angle across from UBN, and UBN is 90 degrees

so is <MBK also 90 degrees? remember the definition of vertical angles

Answer 33

it is

Answer 34

good so A+D are your solution

Answer 35

yikes

let's go through them one by one

look at lines AB + CD. they both are perpendicular to the same line, so using the logic from before are AB and CD parallel, perpendicular, or neither?

Answer 36

they look perpendicular

Answer 37

to me

Answer 38

notice how AB and BC are both perpendicular to GH which, by our earlier problem, means that AB and BC are ~parallel~ to each other

Answer 39

** AB and CD are parallel

Answer 40

ok

Answer 41

using the same logic, AB and EF are also parallel since they're perpendicular to the same line

so so far we have the first two choices selected

Answer 42

AB and CD, and AB and EF are parallel

Answer 43

correct ?

Answer 44

good

Answer 45

now, let's look at IK and KL. they don't give us any angle information or any markings to show parallel and perpendicular so we can't determine anything about them

Answer 46

last one, CD and GH - take a look at the diagram and notice how there's a 90 degree angle between them - does that make them parallel or perpendicular?

Answer 47

perpendicular

Answer 48

awesome so the first two choices are parallel, the third choice is "cannot be determined" and the last choice is perpendicular ~

Answer 49

anyway I need to make lunch for my family, if you have any urgent questions you might be able to ask shadow if he can assist