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# Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC.

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Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135406 [0], given: 12692

Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC. [#permalink]

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17 Oct 2017, 22:43
00:00

Difficulty:

35% (medium)

Question Stats:

79% (00:31) correct 21% (00:25) wrong based on 42 sessions

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Does x = y?

(1) BD is perpendicular to AC.
(2) AB is equal to BC.

[Reveal] Spoiler:
Attachment:

2017-10-18_1042.png [ 8.12 KiB | Viewed 555 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135406 [0], given: 12692

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Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1765

Kudos [?]: 1061 [0], given: 90

Location: India
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Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC. [#permalink]

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18 Oct 2017, 02:41
Bunuel wrote:

Does x = y?

(1) BD is perpendicular to AC.
(2) AB is equal to BC.

[Reveal] Spoiler:
Attachment:
2017-10-18_1042.png

(1) BD is perpendicular to AC.
$$\angle$$ BDA = $$\angle$$ BDC
Not sufficient

(2) AB is equal to BC.
Not sufficient

Combining 1 and 2 , we get
$$\triangle$$ BDA and BDC are congruent (RHS congruency )
$$\angle$$ BDA = $$\angle$$ BDC
AB=BC
BD=BD (Common side)

=>x=y (Corresponding parts of congruent triangles)

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Kudos [?]: 1061 [0], given: 90

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Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC. [#permalink]

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18 Oct 2017, 02:48
Bunuel wrote:

Does x = y?

(1) BD is perpendicular to AC.
(2) AB is equal to BC.

[Reveal] Spoiler:
Attachment:
2017-10-18_1042.png

Sum of the 3 angles equal 180. Combining 1st and 2nd statements, we get y=x . Triangles ABD and Traingles BDC are equal
Ans C

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Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC. [#permalink]

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18 Oct 2017, 07:19
1- This tells us that BD is perpendicular to AC but doesn't mention whether AD=DC.(Insufficient)
2-AB=BC which tells us that. (insufficient)
combining both we find that BD is the perpendicular bisector which means that x=y.
Ans- C

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Re: Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC. [#permalink]

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23 Oct 2017, 17:14
I said B, which I know is wrong. This is an example of me moving too fast and making an assumption. This is the silly mistake I am really trying to avoid making. In statement 2, nowhere does it say that BC bisects the base, but for some reason I assumed it did.

Simple mistakes are killing me.
_________________

I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

Also, I appreciate any kudos.

Kudos [?]: 8 [0], given: 18

Re: Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC.   [#permalink] 23 Oct 2017, 17:14
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# Does x = y? (1) BD is perpendicular to AC. (2) AB is equal to BC.

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