Is quadrilateral RSTV a rectangle?
(1) The measure of ∠RST is 90 degrees
(2) The measure of ∠TVR is 90 degrees
(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.heshamelaziry wrote:Is quadrilateral RSTV a rectangle?
(1) The measure of ∠RST is 90 degrees
(2) The measure of ∠TVR is 90 degrees
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.
