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01 Nov 2007, 10:40
Kudos
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In triangle ABC below, what is the length of side BC?
1, Line segment AD has length 6
2, x = 36
Answer is a, Statement (1) Alone is sufficient. But don't know how, please explain.
thanks in advance!!
Regards,
Pinal
1, Line segment AD has length 6
2, x = 36
Answer is a, Statement (1) Alone is sufficient. But don't know how, please explain.
thanks in advance!!
Regards,
Pinal
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01 Nov 2007, 11:31
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ok you know that <BDC and <ADB ar esupplementary angles so that means <ADB = 180-2x
now you konw that all the angles in ADB have to addup to 180
so <ABD = 180 - (x + 180-2x) = x
so since <ABD = <DAB = x, if you know AD is 6, then you also know that BD is 6 too.
so <BCD = 2x corresponds to the side length of x, the side length of BC corresponds to angle <BDC, which is also 2x, thus is would be 6 too.
now you konw that all the angles in ADB have to addup to 180
so <ABD = 180 - (x + 180-2x) = x
so since <ABD = <DAB = x, if you know AD is 6, then you also know that BD is 6 too.
so <BCD = 2x corresponds to the side length of x, the side length of BC corresponds to angle <BDC, which is also 2x, thus is would be 6 too.
01 Nov 2007, 13:20
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U must know b/f doing this problem certain rules of triangles and angles.
Lets say the triangle to the far left has angle measures of x z and y.
z is the angle at the top and y is the right bottom angle.
knowing line rules, y+2x=180 also x+z+y=180
y=180-2x ---> x+z-2x+180 = 180 so z-x=0. This means that z-x are the same value.
I just did this to show what the following rule is: the outside value (2x) is equal to angles x+z. This rule always holds for triangles and you should know it!
Now since z=x we know that BD is 6, which corresponds to angle z and since angle z=x. angle x corresponds to length of 6 as well.
S2: is garbage.
A.
Lets say the triangle to the far left has angle measures of x z and y.
z is the angle at the top and y is the right bottom angle.
knowing line rules, y+2x=180 also x+z+y=180
y=180-2x ---> x+z-2x+180 = 180 so z-x=0. This means that z-x are the same value.
I just did this to show what the following rule is: the outside value (2x) is equal to angles x+z. This rule always holds for triangles and you should know it!
Now since z=x we know that BD is 6, which corresponds to angle z and since angle z=x. angle x corresponds to length of 6 as well.
S2: is garbage.
A.
