Lines, Angles, & Triangles - SAT Math
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Lines AD and BE intersect at point C as pictured. Which of the following ratios is equal to the ratio of the length of line segment AB to the length of line segment AC?
Lines AD and BE intersect at point C as pictured. Which of the following ratios is equal to the ratio of the length of line segment AB to the length of line segment AC?
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The two triangles ABC and CED are similar (they share the vertical angle at C and each has a right angle). This means their side lengths are proportional. AB to AC maps to ED to CD in the similar triangle.
The two triangles ABC and CED are similar (they share the vertical angle at C and each has a right angle). This means their side lengths are proportional. AB to AC maps to ED to CD in the similar triangle.
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.
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Acute (all $<90^{\circ}$), Right ($=90^{\circ}$), Obtuse (one $>90^{\circ}$).
Acute (all $<90^{\circ}$), Right ($=90^{\circ}$), Obtuse (one $>90^{\circ}$).
Definition of a rectangle.
Definition of a rectangle.
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A parallelogram with four right angles.
A parallelogram with four right angles.
Determine slope of line perpendicular to y = (\t$\frac{1}{2}$)x - 7.
Determine slope of line perpendicular to y = (\t$\frac{1}{2}$)x - 7.
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-2
-2
Find equation of line through (4, 7) parallel to y = -2x + 3.
Find equation of line through (4, 7) parallel to y = -2x + 3.
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$Same slope ⇒ y - 7 = -2(x - 4) ⇒ y = -2x + 15.$
$Same slope ⇒ y - 7 = -2(x - 4) ⇒ y = -2x + 15.$
Formula for midpoint between $(x_1, y_1)$ and $(x_2, y_2)$.
Formula for midpoint between $(x_1, y_1)$ and $(x_2, y_2)$.
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$M = (\tfrac{x_1 + x_2}{2}, \tfrac{y_1 + y_2}{2})$.
$M = (\tfrac{x_1 + x_2}{2}, \tfrac{y_1 + y_2}{2})$.
How can you determine parallel lines in slope-intercept form?
How can you determine parallel lines in slope-intercept form?
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They have the same slope $(m_1 = m_2).$
They have the same slope $(m_1 = m_2).$
How can you determine perpendicular lines in slope-intercept form?
How can you determine perpendicular lines in slope-intercept form?
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Their slopes are negative reciprocals: $m_1 m_2 = -1$.
Their slopes are negative reciprocals: $m_1 m_2 = -1$.
How do you find the midpoint between $(x_1, y_1)$ and $(x_2, y_2)$?
How do you find the midpoint between $(x_1, y_1)$ and $(x_2, y_2)$?
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$((x_1 + x_2)/2, (y_1 + y_2)/2).$
$((x_1 + x_2)/2, (y_1 + y_2)/2).$
How many sides are equal in equilateral, isosceles, and scalene triangles?
How many sides are equal in equilateral, isosceles, and scalene triangles?
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Equilateral (3 equal sides), Isosceles (2 equal sides), Scalene (no equal sides).
Equilateral (3 equal sides), Isosceles (2 equal sides), Scalene (no equal sides).
If a triangle has sides 7, 24, and 25, is it right?
If a triangle has sides 7, 24, and 25, is it right?
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Yes, $7^2 + 24^2 = 49 + 576 = 625 = 25^2$.
Yes, $7^2 + 24^2 = 49 + 576 = 625 = 25^2$.
If two lines are perpendicular, what is the measure of each angle formed?
If two lines are perpendicular, what is the measure of each angle formed?
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$90^{\circ}$.
$90^{\circ}$.
Measure of one interior angle of a regular polygon.
Measure of one interior angle of a regular polygon.
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$\frac{(n - 2)\times180^{\circ}}{n}$.
$\frac{(n - 2)\times180^{\circ}}{n}$.
Properties of a parallelogram.
Properties of a parallelogram.
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Opposite sides and angles are equal; diagonals bisect each other.
Opposite sides and angles are equal; diagonals bisect each other.
Relationship between an inscribed angle and its intercepted arc.
Relationship between an inscribed angle and its intercepted arc.
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An inscribed angle measures half its intercepted arc.
An inscribed angle measures half its intercepted arc.
Angles formed by a transversal cutting parallel lines.
Angles formed by a transversal cutting parallel lines.
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Corresponding angles are congruent, alternate interior angles are congruent, and same-side interior angles are supplementary.
Corresponding angles are congruent, alternate interior angles are congruent, and same-side interior angles are supplementary.
Sum of angles on a straight line.
Sum of angles on a straight line.
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$180^{\circ}$.
$180^{\circ}$.
Sum of exterior angles of any polygon.
Sum of exterior angles of any polygon.
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$360^{\circ}$.
$360^{\circ}$.
Sum of interior angles of an n-sided polygon.
Sum of interior angles of an n-sided polygon.
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$(n - 2)\times180^{\circ}$.
$(n - 2)\times180^{\circ}$.
What are complementary angles?
What are complementary angles?
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Two angles whose measures add up to $90^{\circ}$.
Two angles whose measures add up to $90^{\circ}$.
What are supplementary angles?
What are supplementary angles?
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Two angles whose measures add up to $180^{\circ}$.
Two angles whose measures add up to $180^{\circ}$.
What are vertical angles?
What are vertical angles?
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Opposite angles formed by two intersecting lines; they are congruent.
Opposite angles formed by two intersecting lines; they are congruent.
What is an altitude of a triangle?
What is an altitude of a triangle?
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A perpendicular segment from a vertex to the opposite side.
A perpendicular segment from a vertex to the opposite side.
What is an angle of depression?
What is an angle of depression?
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The angle formed by a horizontal line and the line of sight looking down.
The angle formed by a horizontal line and the line of sight looking down.
What is an angle of elevation?
What is an angle of elevation?
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The angle formed by a horizontal line and the line of sight looking up.
The angle formed by a horizontal line and the line of sight looking up.
What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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$A = \tfrac{1}{2}bh$.
$A = \tfrac{1}{2}bh$.
What is the sum of the interior angles of a triangle?
What is the sum of the interior angles of a triangle?
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$180^{\circ}$.
$180^{\circ}$.
What side is opposite the largest angle in a triangle?
What side is opposite the largest angle in a triangle?
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The longest side.
The longest side.
What side is opposite the smallest angle in a triangle?
What side is opposite the smallest angle in a triangle?
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The shortest side.
The shortest side.
Sum of angles around a point.
Sum of angles around a point.
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$360^{\circ}$.
$360^{\circ}$.