All SAT Math Resources
Example Questions
Example Question #21 : Acute / Obtuse Triangles
Given with and .
Which of the following could be the correct ordering of the lengths of the sides of the triangle?
I)
II)
III)
II only
II or III only
I only
I or II only
III only
II or III only
Given two angles of unequal measure in a triangle, the side opposite the greater angle is longer than the side opposite the other angle.
If were the angle of greatest measure, then , and
.
Since the measures of the angles must total , cannot have the greatest measure.
, so we can explore two other possibilities:
, which here is possible if, for example,
and - since ; and,
, which here is possible if, for example,
and - since .
If , then ; if , then .
This makes the correct response II or III only.
Example Question #152 : Geometry
Which of the given answers choices could NOT represent the sides of a triangle?
All of the given answers could represent the sides of a triangle.
In order for three lengths to represent the sides of a triangle, they must pass the Triangle Inequality.
This means that the sum of any two sides of the triangle must exceed the length of the third side.
With the given answers, the one set of lengths that fail this test is .
Therefore, the lengths could not represent the sides of a triangle.