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

@AZ one more time

Answer 2

is it confusing???

Answer 3

Hi @gokrazy223 , perhaps I can try helping you!

In this picture, there are only two triangles. But we want to make sure we are naming them correctly when we are answering Part A

how do you think we can name those two triangles?

Answer 4

what do you mean by name

Answer 5

Like... the triangle on the left is called GBC

Answer 6

EPB

Answer 7

we want to name the triangle on the right in the same order so that B is the in middle, the angle that is similar to G is the first letter and the angle that is similar to C is the last letter

Answer 8

Angles G and E in their respective triangles are equal

Angles B and B in their respective triangles are equal

Angles C and P in their respective triangles are equal

so if I name a GBC, I want to make sure the letters in the other triangle match that order

Answer 9

so would it be BPE

Answer 10

idk this is confusing

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
Angles G and E in their respective triangles are equal

Angles B and B in their respective triangles are equal

Angles C and P in their respective triangles are equal

so if I name a GBC, I want to make sure the letters in the other triangle match that order
\(\color{#0cbb34}{\text{End of Quote}}\)

GBC would match with EBP

Answer 12

i was close

Answer 13

yes

now, can you tell me WHY is angle CBG equal to angle PBE ?

Answer 14

idk they have 2 corresponding angles

Answer 15

Why are these two angles (that I have marked) equal?

Answer 16

i dont know

Answer 17

i truely dont know im not good at math math will not be one of the subjects in good in\

Answer 18

Here are your options: https://mathbitsnotebook.com/Geometry/ParallelPerp/PPangles.html

Answer 19

cause the angle is congruent ig

Answer 20

angle CBG equal to angle PBE because they are vertical angles

amazing

now, why are these angles equal to each other?

Answer 21

here's a hint

Answer 22

they are interior angles

Answer 23

you missed a word

Answer 24

alternate

Answer 25

ok to put it into a sentence
what angles are equal and why?

Answer 26

what angles are they

Answer 27

<CGB and <PEB

Answer 28

angle CBG equal to angle PBE because they are vertical angles

Answer 29

ok and?
there's another pair that are alternate interior angles

Answer 30

how would i put that in there show me

Answer 31

\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
<CGB and <PEB
\(\color{#0cbb34}{\text{End of Quote}}\)

\(\color{#0cbb34}{\text{Originally Posted by}}\) gokrazy223
alternate
\(\color{#0cbb34}{\text{End of Quote}}\)

\(\color{#0cbb34}{\text{Originally Posted by}}\) gokrazy223
they are interior angles
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 32

CBG and PEB are equal cause they a alternate interior angles

Answer 33

CGB and PEB because they are alternate interior angles
^^ order of the letters matter

Answer 34

but yes, that's correct

Answer 35

ohhhh i thought we was still doing CBG

Answer 36

these two angles are also alternate interior angles

what are those two angles called?

Answer 37

i have no clue

Answer 38

What letter is located at the red marking?

Answer 39

c

Answer 40

ok, and what are the two closest letters to c?

Answer 41

gb

Answer 42

perfect, so C goes in the middle
then the name of that one angle is GCB

Answer 43

using that same idea, what is the name of the other angle?

Answer 44

BPE

Answer 45

perfect
and those two angles are equal because they are alternate interior angles

how would you write that in a sentence?

Answer 46

GCB and BPE are equal because they are alternate interior angles

Answer 47

you are awesome

\(\color{#0cbb34}{\text{Originally Posted by}}\) gokrazy223
angle CBG equal to angle PBE because they are vertical angles
\(\color{#0cbb34}{\text{End of Quote}}\)

\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
CGB and PEB because they are alternate interior angles
^^ order of the letters matter
\(\color{#0cbb34}{\text{End of Quote}}\)

\(\color{#0cbb34}{\text{Originally Posted by}}\) gokrazy223
GCB and BPE are equal because they are alternate interior angles
\(\color{#0cbb34}{\text{End of Quote}}\)

This is what we have so far for our explanation for Part B

Answer 48

on to the hard part

Answer 49

You still need to say in part B that these angles are all equal means that we can use the AA Triangle Similarity Postulate

Answer 50

ok, now we can move to part C

We are looking for... What number times 350 equals 250?

Answer 51

ummmm

Answer 52

that doesnt go together

Answer 53

\(x \times 350 = 250\)

Answer 54

i got a decimal

Answer 55

yes

Answer 56

0.714285

Answer 57

that is called our scale factor

the side BE is equal to 450 times that number

the side PE is equal to 400 times that number

Answer 58

huh???

Answer 59

...

Answer 60

450 times "0.714285"

Answer 61

i got a long number

Answer 62

round it

Answer 63

322

Answer 64

you rounded too much... and in the wrong direction
321.429 is the answer for the length of BE

Answer 65

let's do PE next

what is 400 times "0.714285"

Answer 66

285.714

Answer 67

that's your answer for PE

congratulations

Answer 68

thank you

Answer 69

good luck with math, you're gonna need it

Answer 70

i know i will lol