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Example Questions
Example Question #591 : Psat Mathematics
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 acuteIII)
is a right angleI, II, and III
I and II only
None of these
I and III only
II 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 : 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 #591 : Psat Mathematics
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 #1 : 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 .Example Question #1 : How To Find A Ray
Refer to the above figure.
Which of the following segments is a diagonal of Pentagon
?
A diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon. Of the five choices, only
fits this description.All PSAT Math Resources
