Interpreting Angles/Right Triangles/Rectangles

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mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Sun Oct 25, 2015 5:49 am

I don't want to ask the entire question as I still want to answer it myself. However, there is something (a step) I would like to confirm that I have encountered in the question.

Suppose there is a figure ABCD that very much looks like a rectangle. We are given: ANGLE BAD is 90 degrees; ANGLE BCD is also 90 degrees. Can I assume that the figure is a rectangle?

My take: I think not. What if ANGLE ABC and ANGLE ADC are not 90 degrees each? I have no way to know. Am I right? (There is also a diagonal drawn, from B to D, and I know the value of ONE of the angles (say, DBC) inside the resultant triangle BCD, but I am not even going there yet.) Based on this information that I have, is my conclusion right? I would be grateful for any insights.

Kindly shed some light. My attempt at the figure, below:

B_______________________________C
| |
| |
| |
|_____________ __________________|
A D

Last edited by mindful on Sun Oct 25, 2015 5:54 am, edited 2 times in total.

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Source: Beat The GMAT — Problem Solving | Sun Oct 25, 2015 5:49 am

mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Sun Oct 25, 2015 5:51 am

Whoops. The figure didn't quite come out the way I intended it to (though when I constructed it, it looked fine.) Hope you can figure out the labelling anyway.

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sun Oct 25, 2015 6:15 am

mindful wrote:I don't want to ask the entire question as I still want to answer it myself. However, there is something (a step) I would like to confirm that I have encountered in the question.

Suppose there is a figure ABCD that very much looks like a rectangle. We are given: ANGLE BAD is 90 degrees; ANGLE BCD is also 90 degrees. Can I assume that the figure is a rectangle?

No you cannot assume that the figure is a rectangle. See pic.

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mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Sun Oct 25, 2015 6:31 am

Thought so! Thank you!

Now what if BD was 2; and DC was 1. Does that change things at all?

My guess: No. All it tells me is that BC is Root 3, and the angles in Triangle BDC are 30-60-90 (with Angle DBC being 30, and so on). Can I deduce anything about angles in Triangle ADB, except that the sum of ANGLE ABD and ANGLE BDA is 90 degrees? Kindly enlighten.

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sun Oct 25, 2015 7:06 am

mindful wrote:Thought so! Thank you! Now what if BD was 2; and DC was 1. Does that change things at all?

My guess: No. All it tells me is that BC is Root 3, and the angles in Triangle BDC are 30-60-90 (with Angle DBC being 30, and so on). Can I deduce anything about angles in Triangle ADB, except that the sum of ANGLE ABD and ANGLE BDA is 90 degrees? Kindly enlighten.

Your reasoning is correct: it does not change anything and all we can say about the other triangle is that all the angles sum to 180 degrees

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Sun Oct 25, 2015 10:12 pm

mindful wrote:Thought so! Thank you! Now what if BD was 2; and DC was 1. Does that change things at all?

My guess: No. All it tells me is that BC is Root 3, and the angles in Triangle BDC are 30-60-90 (with Angle DBC being 30, and so on). Can I deduce anything about angles in Triangle ADB, except that the sum of ANGLE ABD and ANGLE BDA is 90 degrees? Kindly enlighten.

Here's some visual confirmation of your suspicion: as you can see, all you're doing is grafting another right triangle on the hypotenuse of a 30-60-90.

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mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Sun Oct 25, 2015 11:57 pm

Thanks everyone!

The figures really clarify it all.

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