All PSAT Math Resources
Example Questions
Example Question #591 : Geometry
Refer to the above figure. You are given that and . Which of the following statements would be sufficient to prove that is a right angle, given what is already known?
I)
II) and are both acute
III) is a right angle
I, II, and III
None of these
I and II only
II and III only
I and III only
I and III only
If , then has short sides and long side . Since
,
then, by the converse of the Pythagorean Theorem, is a right triangle with right angle . Statement I is sufficient.
If and are both acute,we know nothing about ; every triangle has at least two acute angles regardless of type. Statement II tells us nothing.
and form a linear pair and are therefore supplementary. If one is a right angle, so is the other. Therefore, if is a right angle, so is . Statement III is sufficient.
The correct response is Statement I and III only.
Example Question #2 : How To Find The Angle Of Two Lines
Note:
Refer to the above diagram. and which other angle form a pair of corresponding angles?
Two angles formed by a transversal line crossing two other lines are corresponding angles if, relative to the points of intersection, they are in the same position. is formed by the intersection of transversal and ; the angle in the same relative position where intersects is .
Example Question #1 : How To Find The Angle Of Two Lines
Refer to the above diagram. and which other angle form a pair of alternate interior angles?
Two angles formed by a transversal line crossing two other lines are alternate interior angles if:
I) Both angles have their interiors between the lines crossed
II) The angles have their interiors on the opposite sides of the transversal.
Of the given choices, only fits the description; the interior of each is between and , and the interiors are on the opposite sides of .
Example Question #2 : How To Find The Angle Of Two Lines
Refer to the above diagram.
and which other angle form a pair of vertical angles?
Two angles are vertical angles if they share a vertex, anf if their union is a pair of intersecting lines. Of the five choices, only fits both descriptions with .