Geometry – Complete Solutions Manual
90° - answers The sum of an angle and its complement is _____?
Parallel - answers A line which joins the midpoints of two sides of a triangle is _____ to
the third side.
Trapezoid - answers A quadrilateral that has only two sides parallel is a(n) _____.
Perpendicular - answers A line parallel to one of two perpendicular lines is _____ to the
other line.
Radii (or diameters) - answers Two circles are congruent if they have equal _____.
Right - answers An angle inscribed in a semicircle is a(n) _____ angle.
Parallel - answers Tangents to a circle at opposite ends of a diameter are _____ to
each other.
Secant - answers A line that intersects a circle in two points is a(n) _____.
Bisect - answers A diameter that is perpendicular to a chord will _____ the chord.
540° (or 3 straight angles)
(n-2) 180° = (5-2) 180° = 3 × 180° = 540° - answers The sum of the interior angles of a
pentagon is _____. Show your work.
2 (x + 2) = 2 - answers x = -1
3 (5x - 2) + 2 = 26 - answers x = 2
5 (n + 2) = 3n - answers x = -5
5 (5 - x) = -5 - answers x = 6
1+ 4 (2x + 1) = 5 - answers x = 0
x + 3 = 3 (11 - 3x) - answers x = 3
2x - 4 = -4 (x - 5) - answers x = 4
3x = 2 (7 + 5x) - answers x = -2
,2 (3x + 1) = 7x - 5 - answers x = 7
2 (x + 1) = 6x - 46 - answers x = 12
7 (2 - x) - 5= 30 - answers x = -3
5 (x - 6) = 3 + 8 (x + 9) - answers x = -35
245 = -5 (4x - 17) - answers x = -8
17 (3x + 2) = -272 - answers x = -6
5 (7x - 13) = -30 - answers x = 1
12 (-2x - 9) = -12 - answers x = -4
-10 (-4x + 7) = 130 - answers x = 5
-210 = -7 (9x - 60) - answers x = 10
12 (-x + 5) = 144 - answers x = -7
9 (-4x - 29) = 99 - answers x = -10
32 - answers x-7 = 25
-5 - answers 3x + 12 = -3
4 - answers 5x - 7 = 13
10 - answers 3x -30 =0
5 - answers 5 - 3x = -10
-13 - answers 2x + 9 = x - 4
1 - answers 3x - 7 = 5x - 9
-2 - answers 4x + 5 = -2x -7
2 - answers 12x - 9 = 2x + 11
3 - answers 7(x - 4) = - 7
6 - answers 5(x+2) = 40
,7 - answers 3x + 4 = 25
variable - answers A letter used to represent one or more numbers
equation - answers Uses an equal sign to show that two expressions are equal
balance - answers Equal weight
inverse - answers opposite
inverse operation of multiplication - answers Division
inverse operation of division - answers multiplication
inverse operation of addition - answers subtraction
inverse operation of subtraction - answers addition
Distribute 4 - answers What is the first step to solve 4(3x + 2) = 28 ?
Add 11 to both sides. - answers What is the first step to solve 8x - 11 = 34 ?
Multiply by 4 to both sides. - answers What is the second step to solve x/4 - 7 = 12 ?
Divide by 8 to both sides. - answers What is the second step to solve 8x - 11 = 34 ?
Add 7 to both sides. - answers What is the first step to solve x/4 - 7 = 12 ?
Distribute 9 - answers What is the first step to solve 9(5x - 4) = 81 ?
Subtract 4 to both sides - answers What is the first step to solve 4 + 5x = 19 ?
Divide by 5 to both sides. - answers What is the second step to solve 4 + 5x = 19 ?
Distribute 11 - answers What is the first step to solve 11(5 + 4x) = 55 ?
Add 3 to both sides. - answers What is the first step to solve 8 = n/7 - 3 ?
Multipy by 7 to both sides. - answers What is the second step to solve 8 = n/7 - 3 ?
Distribute 4 - answers What is the final step to solve 4(3x + 2) = 28 ?
Distance formula on a coordinate plane - answers d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Horizontal distance - answers d = | x2 -x1|
Vertical Distance - answers d = |y2 -y1|
, Pythagorean Theorem - answers a²+b²=c² (another way to find distance on triangles)
Midpoint formula on a coordinate plane - answers M = ((x₁+x₂)/2, (y₁+y₂)/2)
Partition formula - answers (Px,Py) = ((M(x2)+N(x1))/(M+N) ,(M(y2)+N(y1))/(M+N)) or
1.Find fraction 2. Distance between x's and y's then multiply by fraction. 3. Take INITIAL
point and add the 'fraction of distance'.
ORDER MATTERS
Sum of the Exterior Angles of a Polygon - answers Sum = 360 degrees
sum of interior angles of a polygon - answers Sum = 180(n-2)
One interior angle of a regular polygon - answers 1 angle = (n-2)180/n
One exterior angle of a regular polygon - answers 1 angle = 360/n
Translation Rule - answers (x,y)->(x+a, y+b)
Rotate 90° - answers (x,y)->(-y,x)
Switch and change the FIRST
Remember - Implies CCW
rotate 180° - answers (x,y)->(-x,-y)
Negate Both
Rotate 270° - answers (x,y)->(y,-x)
Switch and change the SECOND
Remember implies CCW
Reflect across y = x - answers (x,y)->(y,x)
JUST SWITCH
Reflect across y = -x - answers (x,y)->(-y,-x)
Switch and Negate BOTH
Total degrees in a Triangle (triangle sum) - answers Sum of THREE angles = 180°
Exterior Angle of a Triangle Theorem - answers The measure of an exterior angle of a
triangle equals the sum of the measures of the two REMOTE INTERIOR angles
Equilateral Triangle Corollary - answers If a triangle is equilateral, then it is equiangular
Equilateral Triangle Theorem - answers If a triangle is equilateral, then it is also
equiangular. Each angle is 60° and all sides congruent.
90° - answers The sum of an angle and its complement is _____?
Parallel - answers A line which joins the midpoints of two sides of a triangle is _____ to
the third side.
Trapezoid - answers A quadrilateral that has only two sides parallel is a(n) _____.
Perpendicular - answers A line parallel to one of two perpendicular lines is _____ to the
other line.
Radii (or diameters) - answers Two circles are congruent if they have equal _____.
Right - answers An angle inscribed in a semicircle is a(n) _____ angle.
Parallel - answers Tangents to a circle at opposite ends of a diameter are _____ to
each other.
Secant - answers A line that intersects a circle in two points is a(n) _____.
Bisect - answers A diameter that is perpendicular to a chord will _____ the chord.
540° (or 3 straight angles)
(n-2) 180° = (5-2) 180° = 3 × 180° = 540° - answers The sum of the interior angles of a
pentagon is _____. Show your work.
2 (x + 2) = 2 - answers x = -1
3 (5x - 2) + 2 = 26 - answers x = 2
5 (n + 2) = 3n - answers x = -5
5 (5 - x) = -5 - answers x = 6
1+ 4 (2x + 1) = 5 - answers x = 0
x + 3 = 3 (11 - 3x) - answers x = 3
2x - 4 = -4 (x - 5) - answers x = 4
3x = 2 (7 + 5x) - answers x = -2
,2 (3x + 1) = 7x - 5 - answers x = 7
2 (x + 1) = 6x - 46 - answers x = 12
7 (2 - x) - 5= 30 - answers x = -3
5 (x - 6) = 3 + 8 (x + 9) - answers x = -35
245 = -5 (4x - 17) - answers x = -8
17 (3x + 2) = -272 - answers x = -6
5 (7x - 13) = -30 - answers x = 1
12 (-2x - 9) = -12 - answers x = -4
-10 (-4x + 7) = 130 - answers x = 5
-210 = -7 (9x - 60) - answers x = 10
12 (-x + 5) = 144 - answers x = -7
9 (-4x - 29) = 99 - answers x = -10
32 - answers x-7 = 25
-5 - answers 3x + 12 = -3
4 - answers 5x - 7 = 13
10 - answers 3x -30 =0
5 - answers 5 - 3x = -10
-13 - answers 2x + 9 = x - 4
1 - answers 3x - 7 = 5x - 9
-2 - answers 4x + 5 = -2x -7
2 - answers 12x - 9 = 2x + 11
3 - answers 7(x - 4) = - 7
6 - answers 5(x+2) = 40
,7 - answers 3x + 4 = 25
variable - answers A letter used to represent one or more numbers
equation - answers Uses an equal sign to show that two expressions are equal
balance - answers Equal weight
inverse - answers opposite
inverse operation of multiplication - answers Division
inverse operation of division - answers multiplication
inverse operation of addition - answers subtraction
inverse operation of subtraction - answers addition
Distribute 4 - answers What is the first step to solve 4(3x + 2) = 28 ?
Add 11 to both sides. - answers What is the first step to solve 8x - 11 = 34 ?
Multiply by 4 to both sides. - answers What is the second step to solve x/4 - 7 = 12 ?
Divide by 8 to both sides. - answers What is the second step to solve 8x - 11 = 34 ?
Add 7 to both sides. - answers What is the first step to solve x/4 - 7 = 12 ?
Distribute 9 - answers What is the first step to solve 9(5x - 4) = 81 ?
Subtract 4 to both sides - answers What is the first step to solve 4 + 5x = 19 ?
Divide by 5 to both sides. - answers What is the second step to solve 4 + 5x = 19 ?
Distribute 11 - answers What is the first step to solve 11(5 + 4x) = 55 ?
Add 3 to both sides. - answers What is the first step to solve 8 = n/7 - 3 ?
Multipy by 7 to both sides. - answers What is the second step to solve 8 = n/7 - 3 ?
Distribute 4 - answers What is the final step to solve 4(3x + 2) = 28 ?
Distance formula on a coordinate plane - answers d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Horizontal distance - answers d = | x2 -x1|
Vertical Distance - answers d = |y2 -y1|
, Pythagorean Theorem - answers a²+b²=c² (another way to find distance on triangles)
Midpoint formula on a coordinate plane - answers M = ((x₁+x₂)/2, (y₁+y₂)/2)
Partition formula - answers (Px,Py) = ((M(x2)+N(x1))/(M+N) ,(M(y2)+N(y1))/(M+N)) or
1.Find fraction 2. Distance between x's and y's then multiply by fraction. 3. Take INITIAL
point and add the 'fraction of distance'.
ORDER MATTERS
Sum of the Exterior Angles of a Polygon - answers Sum = 360 degrees
sum of interior angles of a polygon - answers Sum = 180(n-2)
One interior angle of a regular polygon - answers 1 angle = (n-2)180/n
One exterior angle of a regular polygon - answers 1 angle = 360/n
Translation Rule - answers (x,y)->(x+a, y+b)
Rotate 90° - answers (x,y)->(-y,x)
Switch and change the FIRST
Remember - Implies CCW
rotate 180° - answers (x,y)->(-x,-y)
Negate Both
Rotate 270° - answers (x,y)->(y,-x)
Switch and change the SECOND
Remember implies CCW
Reflect across y = x - answers (x,y)->(y,x)
JUST SWITCH
Reflect across y = -x - answers (x,y)->(-y,-x)
Switch and Negate BOTH
Total degrees in a Triangle (triangle sum) - answers Sum of THREE angles = 180°
Exterior Angle of a Triangle Theorem - answers The measure of an exterior angle of a
triangle equals the sum of the measures of the two REMOTE INTERIOR angles
Equilateral Triangle Corollary - answers If a triangle is equilateral, then it is equiangular
Equilateral Triangle Theorem - answers If a triangle is equilateral, then it is also
equiangular. Each angle is 60° and all sides congruent.
