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Geometry Honors S1 Final: Properties + Theories + Extra Info

Geometry Honors S1 Final: Properties + Theories + Extra Info
80問 • 2年前
  • Verena
  • 通報

    問題一覧

  • 1

    Addition Property of Equality

    If a=b then a+c=b+c

  • 2

    Subtraction Property of Equality

    If a=b then a-c=b-c

  • 3

    Multiplication Property of Equality

    If a=b then a×c=b×c

  • 4

    Division Property of Equality

    If a=b and c≠0 then a/c=b/c

  • 5

    Reflexive Propety of Equality

    a=a

  • 6

    Substitution Property of Equality

    If a=b then b can replace a in any expression

  • 7

    Transitive Property of Equality

    If a=b and b=c then a=c

  • 8

    Reflexive Property of Congruence

    AB≅AB <A≅<A

  • 9

    Transitive Property of Congruence

    If AB≅CD and CD≅EF then AB≅EF If <A≅<B and <B≅<C then <A≅<C

  • 10

    Segment Addition Postulate

    If three points A, B, and C are collinear (on the same line) and point B is between A and C, then AB+BC=AC

  • 11

    Definition of Midpoint

    A point that lies on a segment and bisects the segment. It divides a segment into two congruent segments.

  • 12

    The Distributive Property

    a(b+c)=ab+ac

  • 13

    Symmetric Property for Equality and Congruence

    If a=b then b=a If AB≅DC then DC≅AB

  • 14

    Angle Addition Postulate

    If point B lies in the interior of <AOC, then m<AOB+m<BOC=m<AOC

  • 15

    Vertical Angles Theorem

    Vertical angles are congruent

  • 16

    Linear Pair Angles are Supplementary

    If two angles form a linear pair, then the sum of their measures are 180°

  • 17

    Definition of Complementary Angles

    Two angles whose measures have sum 90°

  • 18

    Definition of Supplementary Angles

    Two angles whose measures have sum 180°

  • 19

    Definition of Angle Bisector

    A ray that divides an angle into two congruent coplanar angles. Its endpoint is at the angle vertex.

  • 20

    Corresponding Angles Postulate

    Corresponding angles are congruent if the transversal intersects two parallel lines.

  • 21

    SSIA Theorem

    When a transversal intersects two parallel lines, the same side interior angles are supplementary.

  • 22

    AIA Theorem

    When a transversal intersects two parallel lines, the alternate interior angles are congruent.

  • 23

    SSEA Theorem

    When a transversal intersects two parallel lines, the same side exterior angles are supplementary.

  • 24

    AEA Theorem

    When a transversal intersects two parallel lines, the alternate exterior angles are congruent.

  • 25

    Triangle Angle Sum is 180 Degrees

    The three interior angles of a triangle will always have a sum of 180°

  • 26

    All sides are congruent

    Equilateral

  • 27

    Two sides are congruent

    Isoceles

  • 28

    No sides are congruent

    Scalene

  • 29

    All angles are congruent

    Equiangular

  • 30

    One angle is 90°

    Right

  • 31

    One angle is over 90° but below 180°

    Obtuse

  • 32

    One angle is above 0° but below 90°

    Acute

  • 33

    Distance Formula

    d=√((x2-x1)²+(y2-y1)²)

  • 34

    Slope formula

    m=(y2-y1)/(x2-x1)

  • 35

    Which of these are short pythagorean triples?

    3, 4, 5, 5, 12, 13, 8, 15, 17, 7, 24, 25, 9, 40, 41, 12, 35, 37, 11, 60, 61

  • 36

    Rotation 90 degrees clockwise

    (y, -x)

  • 37

    Rotation 90 degrees counterclockwise

    (-y, x)

  • 38

    Rotation 180 degrees

    (-x, -y)

  • 39

    Reflection on the x-axis

    (x, -y)

  • 40

    Reflection on the y-axis

    (-x, y)

  • 41

    Reflection on the line y=x

    (y, x)

  • 42

    Reflection on the line y=-x

    (-y, -x)

  • 43

    Intersection of Medians Center of mass (balancing point) Divides the Medians into 2/3 and 1/3 segments

    Centroid

  • 44

    Intersection of Perpendicular Bisectors Center of a Circle being circumscribed on a triangle Equidistant from each vertex

    Circumcenter

  • 45

    Intersection of Angle Bisectors Center of a Circle being inscribed in a triangle Equidistant from the sides

    Incenter

  • 46

    Midpoints of all sides to the opposite vertex (All 3 makes cool 1/3+2/3 stuff happen)

    Median

  • 47

    Connects midpoint of two sides Parallel to the opposite side and 1/2 of the value of the opposite side

    Midsegment

  • 48

    The biggest angle is across from the biggest side The smallest angle is across from the smallest side

    true

  • 49

    The smallest angle is across from the biggest side The biggest angle is across from the smallest side

    false

  • 50

    In order to be a triangle, the lengths must satisfy...

    a+b>c (c=largest side)

  • 51

    Find the possible third side a, x, b (x=missing side)

    b-a<x<b+a

  • 52

    Pythagreon Theorem

    If a triangle is right, then a²+b²=c²

  • 53

    What is this image?

    The Quadratic Formula

  • 54

    If c²=a²+b² then...

    right triangle

  • 55

    If c²<a²+b² then...

    acute triangle

  • 56

    If c²>a²+b²

    obtuse triangle

  • 57

    Exterior Angle Theorem

    An exterior angle is equal to the sum of the two remote interior angles.

  • 58

    Pick all that are correct for isoceles triangles

    If a triangle is isoceles, then base angles are congruent, If 2 angles in a triangle are congruent, then the triangle is isoceles, In an isoceles triangle, the altitude is the angle bisector and the median

  • 59

    A triangle is equilateral iff it is equiangular, furthermore, the angles are 60 degrees

    true

  • 60

    What does iff mean in a theorem?

    That the theorem and it's converse are true

  • 61

    What theorem is this?

    Side Splitter Theorem

  • 62

    What theorem is this?

    Egg Slicer Theorem

  • 63

    What theorem is this?

    Triangle Angle Bisector Theorem

  • 64

    SSS (congruence and similarity)

    side side side

  • 65

    AA (similarity)

    angle angle

  • 66

    SAS (congruence and similarity)

    side angle side

  • 67

    HL (congruence and similarity)

    hypotenuse leg

  • 68

    ASA (congruence)

    angle side angle

  • 69

    AAS (congruence)

    angle angle side

  • 70

    What is true of congruent and similar triangles?

    congruent=all sides and angles are equal similar=all sides are similar (have the same ratio) and all angles are equal

  • 71

    Select all properties of proportions for a/b=c/d

    ad=bc, a/c=b/d, d/b=c/a, b/a=d/c, a+b/b=c+d/d

  • 72

    What is the Golden Ratio? (L:W) (A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle).

    1.618:1

  • 73

    What is the missing side?

    2

  • 74

    What is the missing side?

    √2

  • 75

    What goes after area?

    units²

  • 76

    What goes after perimeter?

    units

  • 77

    What is this?

    altitude

  • 78

    What is this?

    angle bisector

  • 79

    What is this?

    perpindicalular bisector

  • 80

    What is this?

    median

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    問題一覧

  • 1

    Addition Property of Equality

    If a=b then a+c=b+c

  • 2

    Subtraction Property of Equality

    If a=b then a-c=b-c

  • 3

    Multiplication Property of Equality

    If a=b then a×c=b×c

  • 4

    Division Property of Equality

    If a=b and c≠0 then a/c=b/c

  • 5

    Reflexive Propety of Equality

    a=a

  • 6

    Substitution Property of Equality

    If a=b then b can replace a in any expression

  • 7

    Transitive Property of Equality

    If a=b and b=c then a=c

  • 8

    Reflexive Property of Congruence

    AB≅AB <A≅<A

  • 9

    Transitive Property of Congruence

    If AB≅CD and CD≅EF then AB≅EF If <A≅<B and <B≅<C then <A≅<C

  • 10

    Segment Addition Postulate

    If three points A, B, and C are collinear (on the same line) and point B is between A and C, then AB+BC=AC

  • 11

    Definition of Midpoint

    A point that lies on a segment and bisects the segment. It divides a segment into two congruent segments.

  • 12

    The Distributive Property

    a(b+c)=ab+ac

  • 13

    Symmetric Property for Equality and Congruence

    If a=b then b=a If AB≅DC then DC≅AB

  • 14

    Angle Addition Postulate

    If point B lies in the interior of <AOC, then m<AOB+m<BOC=m<AOC

  • 15

    Vertical Angles Theorem

    Vertical angles are congruent

  • 16

    Linear Pair Angles are Supplementary

    If two angles form a linear pair, then the sum of their measures are 180°

  • 17

    Definition of Complementary Angles

    Two angles whose measures have sum 90°

  • 18

    Definition of Supplementary Angles

    Two angles whose measures have sum 180°

  • 19

    Definition of Angle Bisector

    A ray that divides an angle into two congruent coplanar angles. Its endpoint is at the angle vertex.

  • 20

    Corresponding Angles Postulate

    Corresponding angles are congruent if the transversal intersects two parallel lines.

  • 21

    SSIA Theorem

    When a transversal intersects two parallel lines, the same side interior angles are supplementary.

  • 22

    AIA Theorem

    When a transversal intersects two parallel lines, the alternate interior angles are congruent.

  • 23

    SSEA Theorem

    When a transversal intersects two parallel lines, the same side exterior angles are supplementary.

  • 24

    AEA Theorem

    When a transversal intersects two parallel lines, the alternate exterior angles are congruent.

  • 25

    Triangle Angle Sum is 180 Degrees

    The three interior angles of a triangle will always have a sum of 180°

  • 26

    All sides are congruent

    Equilateral

  • 27

    Two sides are congruent

    Isoceles

  • 28

    No sides are congruent

    Scalene

  • 29

    All angles are congruent

    Equiangular

  • 30

    One angle is 90°

    Right

  • 31

    One angle is over 90° but below 180°

    Obtuse

  • 32

    One angle is above 0° but below 90°

    Acute

  • 33

    Distance Formula

    d=√((x2-x1)²+(y2-y1)²)

  • 34

    Slope formula

    m=(y2-y1)/(x2-x1)

  • 35

    Which of these are short pythagorean triples?

    3, 4, 5, 5, 12, 13, 8, 15, 17, 7, 24, 25, 9, 40, 41, 12, 35, 37, 11, 60, 61

  • 36

    Rotation 90 degrees clockwise

    (y, -x)

  • 37

    Rotation 90 degrees counterclockwise

    (-y, x)

  • 38

    Rotation 180 degrees

    (-x, -y)

  • 39

    Reflection on the x-axis

    (x, -y)

  • 40

    Reflection on the y-axis

    (-x, y)

  • 41

    Reflection on the line y=x

    (y, x)

  • 42

    Reflection on the line y=-x

    (-y, -x)

  • 43

    Intersection of Medians Center of mass (balancing point) Divides the Medians into 2/3 and 1/3 segments

    Centroid

  • 44

    Intersection of Perpendicular Bisectors Center of a Circle being circumscribed on a triangle Equidistant from each vertex

    Circumcenter

  • 45

    Intersection of Angle Bisectors Center of a Circle being inscribed in a triangle Equidistant from the sides

    Incenter

  • 46

    Midpoints of all sides to the opposite vertex (All 3 makes cool 1/3+2/3 stuff happen)

    Median

  • 47

    Connects midpoint of two sides Parallel to the opposite side and 1/2 of the value of the opposite side

    Midsegment

  • 48

    The biggest angle is across from the biggest side The smallest angle is across from the smallest side

    true

  • 49

    The smallest angle is across from the biggest side The biggest angle is across from the smallest side

    false

  • 50

    In order to be a triangle, the lengths must satisfy...

    a+b>c (c=largest side)

  • 51

    Find the possible third side a, x, b (x=missing side)

    b-a<x<b+a

  • 52

    Pythagreon Theorem

    If a triangle is right, then a²+b²=c²

  • 53

    What is this image?

    The Quadratic Formula

  • 54

    If c²=a²+b² then...

    right triangle

  • 55

    If c²<a²+b² then...

    acute triangle

  • 56

    If c²>a²+b²

    obtuse triangle

  • 57

    Exterior Angle Theorem

    An exterior angle is equal to the sum of the two remote interior angles.

  • 58

    Pick all that are correct for isoceles triangles

    If a triangle is isoceles, then base angles are congruent, If 2 angles in a triangle are congruent, then the triangle is isoceles, In an isoceles triangle, the altitude is the angle bisector and the median

  • 59

    A triangle is equilateral iff it is equiangular, furthermore, the angles are 60 degrees

    true

  • 60

    What does iff mean in a theorem?

    That the theorem and it's converse are true

  • 61

    What theorem is this?

    Side Splitter Theorem

  • 62

    What theorem is this?

    Egg Slicer Theorem

  • 63

    What theorem is this?

    Triangle Angle Bisector Theorem

  • 64

    SSS (congruence and similarity)

    side side side

  • 65

    AA (similarity)

    angle angle

  • 66

    SAS (congruence and similarity)

    side angle side

  • 67

    HL (congruence and similarity)

    hypotenuse leg

  • 68

    ASA (congruence)

    angle side angle

  • 69

    AAS (congruence)

    angle angle side

  • 70

    What is true of congruent and similar triangles?

    congruent=all sides and angles are equal similar=all sides are similar (have the same ratio) and all angles are equal

  • 71

    Select all properties of proportions for a/b=c/d

    ad=bc, a/c=b/d, d/b=c/a, b/a=d/c, a+b/b=c+d/d

  • 72

    What is the Golden Ratio? (L:W) (A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle).

    1.618:1

  • 73

    What is the missing side?

    2

  • 74

    What is the missing side?

    √2

  • 75

    What goes after area?

    units²

  • 76

    What goes after perimeter?

    units

  • 77

    What is this?

    altitude

  • 78

    What is this?

    angle bisector

  • 79

    What is this?

    perpindicalular bisector

  • 80

    What is this?

    median