How to find the angle of two lines - PSAT Math
Card 1 of 28
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)
Tap to reveal answer
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.
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Refer to the above diagram.
and which other angle form a pair of vertical angles?
Refer to the above diagram.
Tap to reveal answer
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
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Note: 
Refer to the above diagram. 
and which other angle form a pair of corresponding angles?
Note:
Refer to the above diagram.
Tap to reveal answer
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.
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Refer to the above diagram. 
and which other angle form a pair of alternate interior angles?
Refer to the above diagram.
Tap to reveal answer
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
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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)
Tap to reveal answer
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.
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Refer to the above diagram.
and which other angle form a pair of vertical angles?
Refer to the above diagram.
Tap to reveal answer
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
← Didn't Know|Knew It →
Note:
Refer to the above diagram. and which other angle form a pair of corresponding angles?
Note:
Refer to the above diagram.
Tap to reveal answer
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.
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Refer to the above diagram. and which other angle form a pair of alternate interior angles?
Refer to the above diagram.
Tap to reveal answer
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
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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)
Tap to reveal answer
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.
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Refer to the above diagram.
and which other angle form a pair of vertical angles?
Refer to the above diagram.
Tap to reveal answer
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
← Didn't Know|Knew It →
Note:
Refer to the above diagram. and which other angle form a pair of corresponding angles?
Note:
Refer to the above diagram.
Tap to reveal answer
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.
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Refer to the above diagram. and which other angle form a pair of alternate interior angles?
Refer to the above diagram.
Tap to reveal answer
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
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Refer to the above diagram. and which other angle form a pair of alternate interior angles?
Refer to the above diagram.
Tap to reveal answer
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
← Didn't Know|Knew It →
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)
Tap to reveal answer
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.
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Refer to the above diagram.
and which other angle form a pair of vertical angles?
Refer to the above diagram.
Tap to reveal answer
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
← Didn't Know|Knew It →
Note:
Refer to the above diagram. and which other angle form a pair of corresponding angles?
Note:
Refer to the above diagram.
Tap to reveal answer
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.
← Didn't Know|Knew It →
Refer to the above diagram. and which other angle form a pair of alternate interior angles?
Refer to the above diagram.
Tap to reveal answer
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
← Didn't Know|Knew It →
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)
Tap to reveal answer
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.
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Refer to the above diagram.
and which other angle form a pair of vertical angles?
Refer to the above diagram.
Tap to reveal answer
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
← Didn't Know|Knew It →
Note:
Refer to the above diagram. and which other angle form a pair of corresponding angles?
Note:
Refer to the above diagram.
Tap to reveal answer
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.
← Didn't Know|Knew It →