heshamelaziry wrote:Is quadrilateral RSTV a rectangle?
(1) The measure of ∠RST is 90 degrees
(2) The measure of ∠TVR is 90 degrees
Each statement alone is clearly insufficient. The question really comes down to combining them.
Based on the ordering of the letters, we know that RST and TVR are opposite angles. We certainly could draw a rectangle based on that information, but could we draw any other shape?
So, we really need to answer:
if the opposite angles in a quadrilateral are both 90 degrees, does the shape have to be a rectangle?
The answer turns out to be no. It's tough to demonstrate that without drawing a diagram, but picture two right angle triangles with the same hypotenuse but different legs. We can "glue" the triangles together to form a quadrilateral and, because the legs are different lengths, only the opposite angles will both be 90 degrees.
For example, if our triangles were:
5, 5root3, 10 (30/60/90 degree angles)
and
6, 8, 10 (not 30/60/90 degree angles)
We could glue them together on the 10 side to create a quadrilateral and only the two opposite angles would be 90 degrees (and the sides would be 5, 5root3, 6 and 8, clearly not a rectangle).
So, even after combination our shape may or may not be a rectangle: choose E.
