Question

The diagram below models the layout at a carnival where G, R, P, C, B, and E are various locations on the grounds. GRPC is a parallelogram.

Parallelogram GRPC with point B between C and P forming triangle GCB where GC equals 400 ft, CB equals 350 ft, and GB equals 450 ft, point E is outside parallelogram and segments BE and PE form triangle BPE where BP equals 250 ft.

Part A: Identify a pair of similar triangles. (2 points)

Part B: Explain how you know the triangles from Part A are similar. (4 points)

Part C: Find the distance from B to E and from P to E. Show your work. (4 points)

Answer 1

so what all do u know abt triangles and Parallelograms?

Answer 2

only a bit but I wouldn't mind a review

Answer 3

ok so...

Answer 4

parallelograms opposite sides are congruent. Knowing this you can label the opposite lengths of the parallelogram

Answer 5

part A. ??? @sealake101

Answer 6

i was just saying she said she could use a review on triangles and Parallelograms

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
about alternate interior - exterior congruently angles - did you ve heard ?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 8

and how are these opposite angles in point B ?

Answer 9

@sealake101 please continue i m here just to help you

Answer 10

ok so what exactly r u unsure of

Answer 11

so for part A you need to find a pair of triangles that r similar

Answer 12

yea that's what im trying

Answer 13

did u see the diagram

Answer 14

so there are only 2 triangles in the diagram right

Answer 15

whaich are BPE and GCB

Answer 16

so what would that tell u for part A?

Answer 17

oh I thought it was 3

Answer 18

ok so part B...

Answer 19

now that part A is answered who are they similar?

Answer 20

how*

Answer 21

good job @sealake101 so in this way step by step please explain it - thank you

Answer 22

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
good job @sealake101 so in this way step by step please explain it - thank you
\(\color{#0cbb34}{\text{End of Quote}}\)
yep

Answer 23

ok so like how r they alike ...
if u flip the bottom triangle around so its up ward like triangle GCB what can u tell

Answer 24

so like in your head can you make the triangle BPE fit in GCB?

Answer 25

I could tell their similar by using proportians

Answer 26

ok yeah i didnt know if u were familiar with proportions or not
so how can u tell?

Answer 27

I would have to cross multiply but dk what numbers

Answer 28

ok so CB/CG = PB/PE if that helps

Answer 29

@jhonyy9 is that right?

Answer 30

so just a little attention please

bc. you dont know the length of corresponding sides not can be used the proportionality of corresponding sides

Answer 31

wow I had that written down

Answer 32

it would be 300/350=200/x233+1/3 feet

Answer 33

@sealake101 but using this proportionalitie what you ve wrote above you can calcule the length of side PE

but this not is for part A.

Answer 34

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
@sealake101 but using this proportionalitie what you ve wrote above you can calcule the length of side PE

but this not is for part A.
\(\color{#0cbb34}{\text{End of Quote}}\)
ok

Answer 35

ok little help

what are these similar triangles ?

Answer 36

please collaborate

Answer 37

GCB and EPB are similar triangles is what we agreed on right Kenia

Answer 38

yes

Answer 39

yes

so and now we need to prove the similarity of these triangles

how ?

Answer 40

what you know about 2 opposite angles formed by two lines - how are ?

Answer 41

they are formed by two lines intersecting

Answer 42

yes of corse - so there on this image let be angle B_1 and opposite to this let be angle B_3 - formed by line GE and line CP

Answer 43

how are these angles ?

Answer 44

you typed angle b1 and angle b3?

Answer 45

yes

Answer 46

we not them in this way

Answer 47

@sealake101

Answer 48

ok ?

Answer 49

sorry im trying to do my science too
but yea

Answer 50

ok and did you heard about alternate interior and alternate exterior angles ?

Answer 51

yes, i did

Answer 52

formed by a line and two parallel lines - yes ?

ok so how are these angles ?

Answer 53

on this image there are lines GR and PC - parallel and intersected by line GE

what are there these alternate interior angles what we can use to prove the similarity of these two triangles ?

Answer 54

because of alternate interior angles, it shows that angle G is congruent to angle E

Answer 55

sorry im back

Answer 56

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Kenia
sorry im back
\(\color{#0cbb34}{\text{End of Quote}}\)
ok so do u know about alternate interior and alternate exterior angles ?

Answer 57

yea a bit

Answer 58

wow u really just did that all lol

Answer 59

yes of corse and now look on this image hope will be more understandably about what i talk

Answer 60

@Kenia the similarity of these triangles is clearly now ?

Answer 61

part C. ?

Answer 62

just use the proportionality of corresponding sides

@sealake101

Answer 63

what are these ways ?

Answer 64

wait so what is the answer exactly

Answer 65

where for what ?

Answer 66

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Kenia
wait so what is the answer exactly
\(\color{#0cbb34}{\text{End of Quote}}\)
for part b?

Answer 67

for B

Answer 68

@sealake101 do you can calcule these distances ?

Answer 69

ok so for part B.

@sealake101 can you clarify the similarity of triangles ?

Answer 70

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
ok so for part B.

@sealake101 can you clarify the similarity of triangles ?
\(\color{#0cbb34}{\text{End of Quote}}\)
yeah ok so because of vertical angles are congruent the two angles are congruent...that is what I would put

Answer 71

ok so what similariity theorem was used there than ?

Answer 72

hey ill brb

Answer 73

did you heard about SAS or SSS or ASA ... and so much

Answer 74

@Kenia

Answer 75

yes still learning

Answer 76

ok and in case of your posted problem what theorem we used ?

Answer 77

Idk if it was ASA or SAS

Answer 78

what mean this S from there ?

Answer 79

wym

Answer 80

what mean this ASA ?

Answer 81

so similarity by angle - side - angle

ok ?

Answer 82

yes

Answer 83

and now please look on my above posted image - i ve noted there similar 3 angles - yes ? so without any sides

than in this case what theorem of similarity we can use there ?

Answer 84

so SSS - what mean side-side - side ?

Answer 85

yes side side side postulate

Answer 86

3 angles how you can note ?

Answer 87

no

Answer 88

there are not any sides

Answer 89

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
3 angles how you can note ?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 90

AAA

Answer 91

same with SSS just here we have 3 angles and not sides

ok ?

Answer 92

and now for part C.

Answer 93

wait so

Answer 94

the final is 3 angles with no sides

Answer 95

distance BE and PE

Answer 96

yes angle - angle -angle similarity theorem

Answer 97

sorry i gtg but i come back in a 20 min.

Answer 98

sorry i had to take my puppy outside ...

Answer 99

ok

Answer 100

that's fine

Answer 101

@sealake101 please help continue - and i will come to check it - thank you

Answer 102

ok

Answer 103

ok so r u already on partC ?

Answer 104

yea give me a minute to type this down

Answer 105

ok

Answer 106

u good now?

Answer 107

it wasn't letting me type sorry

Answer 108

yea

Answer 109

ok so what all did u get to for this part?

Answer 110

part C?

Answer 111

yes

Answer 112

we were about to start then he left

Answer 113

ok so finding the distance from B to E and from P to E you will have to find a ratio or proportion

Answer 114

ok

Answer 115

so like what i put up earlier ...

Answer 116

CB/CG = PB/PE

Answer 117

right?

Answer 118

yes I have that

Answer 119

ok did u fill it in yet?

Answer 120

yes

Answer 121

ok what did u get?

Answer 122

300/350=200/x 233+ 1/3 feet

Answer 123

yes

Answer 124

do u know what to do next?

Answer 125

holdup

Answer 126

k

Answer 127

tell me when u get it

Answer 128

I will

Answer 129

kk

Answer 130

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Kenia
300/350=200/x 233+ 1/3 feet
\(\color{#0cbb34}{\text{End of Quote}}\)
wait hold on...

Answer 131

where did u get 300 and 200 it should be 400 and 250...

Answer 132

you're right omg no wonder I was stuck

Answer 133

wait so 400/350=250/x 233?

Answer 134

idk where u got them numbers

Answer 135

400/350=450/250

Answer 136

sorry gtg

Answer 137

oh ok thanks for ur help

Answer 138

ok i m

Answer 139

hiii

Answer 140

did you solved the part C. ?

Answer 141

so far I have CB/CG=PB/PE which is 400/350=250/x 233+ 1/3 feet I just need to solve it

Answer 142

400/350 = 250 /x

yes and now solve this for x

Answer 143

\[\frac{ 400 }{ 350 } = \frac{ 250 }{ x }\]

cross multiplie and so what you get ?

Answer 144

are you here ?

Answer 145

yea im typing it down sorry

Answer 146

so that would be

Answer 147

400x

Answer 148

would I have to multiply 250 and 350

Answer 149

yes 400x = 250*350 and from there how you get the x ?

Answer 150

any idea ?

Answer 151

that would be 87,500

Answer 152

what is this ?

Answer 153

250x350

Answer 154

sorry but i ve dont said to you to multiplie

Answer 155

there is

400x = 250*350

hoe you get the x ?

Answer 156

how

Answer 157

divide both sides by 400 and will get in this way what ?

Answer 158

divide 400 with 250 and 350?

Answer 159

there are

400x = 250*350 divide both sides by 400 and will get

\[\frac{ 400x }{ 400 } = \left( \frac{ 250*350 }{ 400 } \right)\]

Answer 160

and now ?

Answer 161

in the left part simplify the 400 by 400 and remain just x

yes ?

Answer 162

in the right part how will be ?

Answer 163

alo

Answer 164

yes

Answer 165

250*350 / 400 = ?

Answer 166

what can you simplify there ?

Answer 167

I thought it would be x instead of 400

Answer 168

ohh

Answer 169

wait ok

Answer 170

875/4

Answer 171

how you get this ?

Answer 172

250*350 = 25*35*100

yes ?

Answer 173

I input it in the calculator

Answer 174

no in your head

Answer 175

so this is ok ?

25*35*100 in numerator

yes ?

Answer 176

I don't get it

Answer 177

bc. 250 = 25*10
and 350 = 35*10

25*10*35*10 = 25*35*10*10 = 25*35*100

yes ?

Answer 178

ok ?

Answer 179

im still confused

Answer 180

so than there will be

ok this is just for you than you wan make calcule without calculator

Answer 181

so than x = ?

Answer 182

yes

Answer 183

so than PE = ?

Answer 184

um

Answer 185

I still only have 400x/400=(250×350/400)

Answer 186

yes but from there we ve got

x = 250*350/400 = ?

Answer 187

this is the distance of PE

Answer 188

idk how I would calculate that

Answer 189

875/4

have got above

Answer 190

oh so I was right

Answer 191

218,75

and 875/4 = 218,75

yes you was right

Answer 192

so and now the second distance

Answer 193

how you get the BE using proportionality of corresponding sides ?

Answer 194

so that was P to E

Answer 195

yes

Answer 196

ok

Answer 197

and now the BE

Answer 198

what proportional sides can we use for BE ?

Answer 199

look please on the line CP and GE

CP formed by what segments ?
and
GE formed by what segments ?

Answer 200

ge is 450

Answer 201

no this is just GB

Answer 202

ohh

Answer 203

so than you look on this image - you see that

GE formed from GB and BE
and
CP formed from CB and BP

yes ?

Answer 204

ok ?

Answer 205

ok back

Answer 206

so using the proportionality of corresponding sides we can write

GB/BE = CB / BP

Answer 207

so this is different?

Answer 208

why different ?

now you need calcule the distance from B to E

Answer 209

what would the numbers be exactly

Answer 210

GB/BE = CB / BP

substitute the length in this equation for what you know

Answer 211

GB = ?

Answer 212

CB= ?

Answer 213

BP=?

Answer 214

look on this image pls

Answer 215

I am

Answer 216

still a lil confused

Answer 217

you need use the length given from there

Answer 218

ok

Answer 219

than substitute the length what given there inside this

GB/BE = CB / BP

Answer 220

wait

Answer 221

GC/BE= CB/BP you said it was this

Answer 222

no GC there i ve wrote GB

Answer 223

the length of GB = ?

Answer 224

im so confused

Answer 225

ok I input that

Answer 226

GB/BE = CB / BP

so please write these with numbers - lengths what you know

Answer 227

idk the numbers

Answer 228

look on the posted attached image

Answer 229

ok

Answer 230

gb is 450?

Answer 231

GB = 450 ft
CB=350ft
BP=250ft

Answer 232

GB/BE = CB / BP

Answer 233

how you get from there the BE ?

Answer 234

cross multiplie what you get ?

Answer 235

im trying to set them up in fractions

Answer 236

ok

Answer 237

so it would be

Answer 238

450/350=250/x

Answer 239

nor really

450/x = 350/250

Answer 240

so and from these now calcule the x value

Answer 241

cross multiplie what will get ?

Answer 242

350x

Answer 243

350x = ?

Answer 244

450x250?

Answer 245

yes

350x = 450*250

and now from this you need to calcule the x value

Answer 246

that would be 112,500

Answer 247

what ? the x ?

Answer 248

no 450x250

Answer 249

ok but you need the x

Answer 250

350x = 450*250

to get the x separate divide both sides by 350 and will get in this way for x

x = ?

Answer 251

ok so

Answer 252

x = 450*250/350 = ?

Answer 253

so BE = ?

Answer 254

2250/7

Answer 255

450*25/35

450*5/7

2250/7 = ?

Answer 256

BE = ?

Answer 257

just divide the 2250 by 7 and will get the right answer

hope helped

have a nice day

bye bye