All PSAT Math Resources
Example Questions
Example Question #1 :Lines
Refer to the above figure. You are given thatand. Which of the following statements would be sufficient to prove thatis a right angle, given what is already known?
I)
II)andare both acute
III)is a right angle
II and III only
I and II only
I, II, and III
None of these
I and III only
I and III only
If, thenhas short sidesand long side. Since
,
then, by the converse of the Pythagorean Theorem,is a right triangle with right angle. Statement I is sufficient.
Ifandare both acute,we know nothing about; every triangle has at least two acute angles regardless of type. Statement II tells us nothing.
andform a linear pair and are therefore supplementary. If one is a right angle, so is the other. Therefore, ifis a right angle, so is. Statement III is sufficient.
The correct response is Statement I and III only.
Example Question #1 :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 transversaland; the angle in the same relative position whereintersectsis.
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适合description; the interior of each is betweenand, 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, onlyfits both descriptions with.
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