How to find the angle of two lines - PSAT Math
Card 0 of 4
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
Refer to the above figure. You are given that
I)
II)
III)
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.
If
then, by the converse of the Pythagorean Theorem,
If
The correct response is Statement I and III only.
Compare your answer with the correct one above
Refer to the above diagram.
and which other angle form a pair of vertical angles?
Refer to the above diagram.
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 
.
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
Compare your answer with the correct one above
Note: 
Refer to the above diagram. 
and which other angle form a pair of corresponding angles?
Note:
Refer to the above diagram.
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 
.
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.
Compare your answer with the correct one above
Refer to the above diagram. 
and which other angle form a pair of alternate interior angles?
Refer to the above diagram.
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 
.
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
Compare your answer with the correct one above