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D is on side AB of Triangle ABC. We know triangle ABC\(\sim\)triangle ACD and angle A=48. If BC=BD, what is angle B in degrees?

here is the image:

I'll add the pic - Melody

Oct 8, 2021
edited by Melody  Oct 8, 2021

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I get 28 degrees.  (which I have not checked)

Let's see what catmg comes up with.

Oct 9, 2021
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Nice. :))

I really miss going on this forum more often.

=^._.^=

catmg  Oct 9, 2021
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You are the one who did the nice work Catmg.

Yes school is busy, so is life for younger people.

Most of the people who are here a lot, to answer questions I mean, are retired.

It can continue to be a nice hobby for you though :))

Melody  Oct 9, 2021
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It is a very fun hobby.

I quite like working on my math skills and hopefully helping others improve too.

=^._.^=

catmg  Oct 9, 2021
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Thank you so much for the explanation!

CCeed  Oct 9, 2021
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Hello CCeed :))

Let angle B = x

angle A = 48

angle C = 132 - x

Since ABC ~ ACD

angle B = angle ACD = x

angle C = angle CDA = 132 - x

Since BC = BD

BCD = BDC

BCD + BDC + B = 180 degrees

BDC + BDC + x = 180 degrees

BDC = (180-x)/2

CDA  + CDB = 180

132 - x + (180-x)/2 = 180

x = 28

I hope this helped. :))

=^._.^=

Oct 9, 2021
#9
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Thank you too for the explanation! <3

I'm grateful!

CCeed  Oct 9, 2021
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I find it quite difficult to get my head around geometry questions such as this.

So I will give you some insight as to how I go about it.

I drew the diagram and shade the smaller one.

then I said the smallest side of the big triangle is AC which corresponds to the smallest side of the small diagram AD

then I said the biggest side of the big triangle is AB which corresponds to the biggest side of the small diagram AC

Now I draw the corresponding triangles like this:

And then I take it from there.

I suppose it is too slow long term but while you are getting the hang of it it can help.

Oct 9, 2021
#7
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This really does help.

Similar triangles are tricky, especially with remembering which angles correspond to which angles.

I always get them confused so when you do have the time, it's very nice to draw out the triangle so that they face the same way.

=^._.^=

catmg  Oct 9, 2021
#10
+1

https://web2.0calc.com/questions/geometry-help-asap-pls_1#r2

Oct 9, 2021