
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 11th, 2010, 05:32 PM  #1 
Member Joined: Dec 2009 Posts: 66 Thanks: 0  Isosceles Trapezoid
Another question I'm confused on while preparing for state; An isosceles trapezoid has bases of respective lengths 10 and 20. A quadrilateral is formed by joining the midpoints of the consecutive sides of the isosceles trapezoid. If one of the sides of that quadrilateral has a length of 12, the sum of the lengths of the diagonals are...? Thanks in advance, you guys are great 
March 11th, 2010, 05:46 PM  #2 
Member Joined: Dec 2009 Posts: 66 Thanks: 0  Re: Isosceles Trapezoid
Looking at the information, I've recognized that the quadrilateral is a kite, but I'm not sure where to go from there

March 11th, 2010, 06:33 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1619 
The length of one of the diagonals of the quadrilateral may be deduced easily from the length information given for the bases of the trapezoid.

March 11th, 2010, 06:52 PM  #4 
Member Joined: Dec 2009 Posts: 66 Thanks: 0  Re: Isosceles Trapezoid
Ahh, so I think I've recognized it. The answer I got fits the correct answer as well Tell me if my approach here doesn't break any mathematical rules: From the information given I have determined that the figure was a rhombus (why did I do that?), and every side must then be equal to 12 units. Since one of the diagonals of the rhombus went through the median of the trapezoid, it must be the average of the two bases ((20+10)/2 = 15) and since diagonals in a rhombus are perpendicular bisectors, one of four right triangles formed from the intersection of the two diagonals has a length of 15/2 Upon Pythagorean Theorem, the other leg must equal 3 root 39 / 2 Multiplying by two gives the measure of the second diagonal Most of it makes sense to me now, but my final question is how can I be positive that it was in fact a rhombus? At state I don't want to make wrong assumptions and perform calculations leading to the wrong answer 
March 11th, 2010, 07:32 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1619 
Use the midpoint theorem to prove it's a parallelogram, then the symmetry of the diagram implies it's a rhombus.


Tags 
isosceles, trapezoid 
Search tags for this page 
volume of isosceles trapezoid,volume of an isosceles trapezoid formula,do the diagonals of a trapezoid intersect at the median,volume of an isosceles trapezoid,volume of isiscele trapezoid,Volume of a isosceles trapezoid,isosceles trapezoid volume
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Isosceles triangle  lithginte  Algebra  1  May 9th, 2012 06:34 AM 
Volume of a Water Trough (Isosceles Trapezoid)  kittycub4  Calculus  2  October 21st, 2011 03:55 PM 
Isosceles triangle help.  jordanshaw  Algebra  6  January 29th, 2011 04:14 PM 
vertices of isosceles triangle  mad  Algebra  31  August 19th, 2010 05:39 AM 
find the dimension for isosceles trapezoid  dai_lo  Calculus  1  February 27th, 2008 11:45 AM 