Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
can the pt mentioned abt property of right angle triangle be proven
Imagine the right triangle inscribed in circle. We know that if the right triangle is inscribed in circle, hypotenuse must be diameter, hence half of the hypotenuse is radius. The line segment from the third vertex to the center is on the on the one hand radius of the circle=half of the hypotenuse and on the other hand as it's connecting the vertex with the midpoint of the hypotenuse it's median too.
Attachment:
Math_Tri_inscribed.png [ 6.47 KiB | Viewed 7823 times ]
In triangle ABC, AB has a length of 10 and D is the midpoint of AB. What is the length of line segment DC?
(1) Angle C= 90 (2) Angle B= 45
(1) We have right triangle ABC, with right angle at C. Property of right triangle: median from right angle is half of the hypotenuse, hence CD=AB/2=10/2=5. Sufficient.
can the pt mentioned abt property of right angle triangle be proven
Imagine the right triangle inscribed in circle. We know that if the right triangle is inscribed in circle, hypotenuse must be diameter, hence half of the hypotenuse is radius. The line segment from the third vertex to the center is on the on the one hand radius of the circle=half of the hypotenuse and on the other hand as it's connecting the vertex with the midpoint of the hypotenuse it's median too.
Attachment:
Math_Tri_inscribed.png
Hope it's clear.
Thank you for the explanation. The inscribed triangle example helped a lot. Regarding STMT 1, my thought process was that the triangle could be 45-45-90 or 30-60-90, which in my mind, could affect the length of CD. However, from your example or more so the visual, I see that the angles don't matter...that the median is determined by the hypotenuse. Thanks for the lesson learned; basic yet important.
_________________
Re: In triangle ABC, AB has a length of 10 and D is the midpoint
[#permalink]
Show Tags
03 Apr 2014, 07:49
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and CD both have a length of 5 so we actually have two right triangles BDC and ADC.
In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD
Re: In triangle ABC, AB has a length of 10 and D is the midpoint
[#permalink]
Show Tags
03 Apr 2014, 08:32
jlgdr wrote:
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and BD both have a length of 5 so we actually have two right triangles BDC and ADC.
In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD
Where am I going wrong here? Thanks Cheers J
Notice that CD is the median, not the altitude, so we don't know whether triangles BDC and ADC are right angled.
Re: In triangle ABC, AB has a length of 10 and D is the midpoint
[#permalink]
Show Tags
18 May 2017, 21:19
It doesn't make sense - could you please elaborate on why (2) is NS?
Bunuel wrote:
jlgdr wrote:
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and BD both have a length of 5 so we actually have two right triangles BDC and ADC.
In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD
Where am I going wrong here? Thanks Cheers J
Notice that CD is the median, not the altitude, so we don't know whether triangles BDC and ADC are right angled.
Re: In triangle ABC, AB has a length of 10 and D is the midpoint
[#permalink]
Show Tags
18 May 2017, 21:36
1
mdacosta wrote:
It doesn't make sense - could you please elaborate on why (2) is NS?
Bunuel wrote:
jlgdr wrote:
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and BD both have a length of 5 so we actually have two right triangles BDC and ADC.
In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD
Where am I going wrong here? Thanks Cheers J
Notice that CD is the median, not the altitude, so we don't know whether triangles BDC and ADC are right angled.
Does this make sense?
To put it simply: we know the length of a base (10) and one angle at the base (45 degrees). There are infinitely many triangles with this properties, so there are indefinitely many lengths of the median to the base possible.
_________________
close
46% (01:41) correct 
