Geometry and Trigonometry - SAT Math
Card 0 of 111
What is the sum of the interior angles of a triangle?
What is the sum of the interior angles of a triangle?
$180^{\circ}$.
$180^{\circ}$.
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What is the triangle inequality theorem?
What is the triangle inequality theorem?
The sum of any two sides must be greater than the third side.
The sum of any two sides must be greater than the third side.
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How many sides are equal in equilateral, isosceles, and scalene triangles?
How many sides are equal in equilateral, isosceles, and scalene triangles?
Equilateral (3 equal sides), Isosceles (2 equal sides), Scalene (no equal sides).
Equilateral (3 equal sides), Isosceles (2 equal sides), Scalene (no equal sides).
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Define these types of triangles by their angle measures: acute, right, and obtuse.
Define these types of triangles by their angle measures: acute, right, and obtuse.
Acute (all $<90^{\circ}$), Right ($=90^{\circ}$), Obtuse (one $>90^{\circ}$).
Acute (all $<90^{\circ}$), Right ($=90^{\circ}$), Obtuse (one $>90^{\circ}$).
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What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
$A = \tfrac{1}{2}bh$.
$A = \tfrac{1}{2}bh$.
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What is the formula for the area of a triangle using sine?
What is the formula for the area of a triangle using sine?
$A = \tfrac{1}{2}ab\sin C$.
$A = \tfrac{1}{2}ab\sin C$.
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What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
$a^2 + b^2 = c^2$ (for right triangles).
$a^2 + b^2 = c^2$ (for right triangles).
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List the common Pythagorean triples.
List the common Pythagorean triples.
$(3,4,5)$, $(5,12,13)$, $(7,24,25)$, $(8,15,17)$.
$(3,4,5)$, $(5,12,13)$, $(7,24,25)$, $(8,15,17)$.
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What is the hypotenuse?
What is the hypotenuse?
The side opposite the right angle, and the longest side in a right triangle.
The side opposite the right angle, and the longest side in a right triangle.
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What are the sides in a right triangle called?
What are the sides in a right triangle called?
Legs and hypotenuse.
Legs and hypotenuse.
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Special triangle: ratio for $45^{\circ}$–$45^{\circ}$–$90^{\circ}$.
Special triangle: ratio for $45^{\circ}$–$45^{\circ}$–$90^{\circ}$.
$1:1:\sqrt{2}$.
$1:1:\sqrt{2}$.
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Special triangle: ratio for $30^{\circ}$–$60^{\circ}$–$90^{\circ}$.
Special triangle: ratio for $30^{\circ}$–$60^{\circ}$–$90^{\circ}$.
$1:\sqrt{3}:2$ (short leg : long leg : hypotenuse).
$1:\sqrt{3}:2$ (short leg : long leg : hypotenuse).
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What side is opposite the smallest angle in a triangle?
What side is opposite the smallest angle in a triangle?
The shortest side.
The shortest side.
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What side is opposite the largest angle in a triangle?
What side is opposite the largest angle in a triangle?
The longest side.
The longest side.
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What is an altitude of a triangle?
What is an altitude of a triangle?
A perpendicular segment from a vertex to the opposite side.
A perpendicular segment from a vertex to the opposite side.
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Find the hypotenuse if legs are 6 and 8.
Find the hypotenuse if legs are 6 and 8.
$\sqrt{6^2 + 8^2} = 10$.
$\sqrt{6^2 + 8^2} = 10$.
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Find missing leg if $c = 13$, $a = 5$.
Find missing leg if $c = 13$, $a = 5$.
$b = \sqrt{13^2 - 5^2} = 12$.
$b = \sqrt{13^2 - 5^2} = 12$.
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Find the area with base 10 and height 6.
Find the area with base 10 and height 6.
$A = \tfrac{1}{2}(10)(6) = 30$.
$A = \tfrac{1}{2}(10)(6) = 30$.
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In a $30^{\circ}$–$60^{\circ}$–$90^{\circ}$ triangle, if the short leg = 5, find hypotenuse.
In a $30^{\circ}$–$60^{\circ}$–$90^{\circ}$ triangle, if the short leg = 5, find hypotenuse.
$10$.
$10$.
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In a $45^{\circ}$–$45^{\circ}$–$90^{\circ}$ triangle, if a leg = 4, find hypotenuse.
In a $45^{\circ}$–$45^{\circ}$–$90^{\circ}$ triangle, if a leg = 4, find hypotenuse.
$4\sqrt{2}$.
$4\sqrt{2}$.
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