Geometry References And Formulas

Question 1

What is the Midpoint Formula?

Answer 1

The Midpoint Formula is used to find the midpoint between two points in a coordinate plane.

Question 2

What is the Distance Formula?

Answer 2

The Distance Formula is V (x2 - x1)² + (y2 - y1)².

Question 3

What is the Pythagorean Theorem?

Answer 3

The Pythagorean Theorem states that a² + b² = c².

Question 4

What is the Reflexive Property?

Answer 4

The Reflexive Property states that AB = AB or ∠A = ∠A.

Question 5

What is the Transitive Property?

Answer 5

If A = B and B = C, then A = C.

Question 6

What is the formula for Translations?

Answer 6

Translations can be represented as (x + a, y + b) or ⟨a, b⟩.

Question 7

What are the Reflection Rules across the x-axis?

Answer 7

Reflection across the x-axis is (x, y) → (x, -y).

Question 8

What are the Reflection Rules across the y-axis?

Answer 8

Reflection across the y-axis is (x, y) → (-x, y).

Question 9

What are the Reflection Rules across y=x?

Answer 9

Reflection across y=x is (x, y) → (y, x).

Question 10

What are the Reflection Rules across y=-x?

Answer 10

Reflection across y=-x is (x, y) → (-y, -x).

Question 11

What is the rule for 90° counterclockwise rotation?

Answer 11

90° counterclockwise rotation is (x, y) → (-y, x).

Question 12

What is the rule for 180° rotation?

Answer 12

180° rotation is (x, y) → (-x, -y).

Question 13

What is the rule for 270° counterclockwise rotation?

Answer 13

270° counterclockwise rotation is (x, y) → (y, -x).

Question 14

What is the Dilation Rule?

Answer 14

Dilation is represented as (kx, ky) where k is the scale factor.

Example: SF = 2 results in (2x, 2y).

Question 15

What is the Triangle Angle Sum Theorem?

Answer 15

The Triangle Angle Sum Theorem states that ∠1 + ∠2 + ∠3 = 180°.

Question 16

What indicates congruence in figures?

Answer 16

If you can map it using rigid motions (Translations, Reflection, Rotation), then it’s congruent.

Question 17

What are the properties of parallel lines?

Answer 17

Parallel lines have the same slope.

Question 18

What are the properties of perpendicular lines?

Answer 18

Perpendicular lines have slopes that are opposite reciprocals.

Question 19

What are vertical angles?

Answer 19

Vertical angles are congruent.

Question 20

What is the definition of supplementary angles?

Answer 20

Supplementary angles sum to 180°.

Question 21

What is the definition of complementary angles?

Answer 21

Complementary angles sum to 90°.

Question 22

What is a linear pair of angles?

Answer 22

A linear pair consists of two angles on the same line that sum to 180°.

Question 23

What are the properties of angles formed by parallel lines and a transversal?

Answer 23

Corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and same side interior angles sum to 180°.

Question 24

What are the congruence criteria for triangles?

Answer 24

The criteria are SSS, ASA, SAS, AAS, HL.

Question 25

What are the similarity criteria for triangles?

Answer 25

The criteria are AA, SSS, SAS.

Question 26

How do you find the scale factor?

Answer 26

Use proportions to find the scale factor.

Question 27

What is the Polygon Angle Sum Theorem?

Answer 27

The Polygon Angle Sum Theorem is (n - 2) • 180, where n is the number of sides.

Question 28

What characterizes an isosceles triangle?

Answer 28

An isosceles triangle has 2 congruent sides and base angles that are equal.

Question 29

What characterizes an equilateral triangle?

Answer 29

An equilateral triangle has 3 congruent sides and all angles equal 60°.

Question 30

What is the Triangle Inequality Theorem?

Answer 30

The Triangle Inequality Theorem states that a + b > c.

Question 31

What is the Triangle Hinge Theorem?

Answer 31

The Triangle Hinge Theorem states that if you add two sides and subtract two sides, the third side is between those two results. ## Footnote Example: For sides 5 and 12, add = 17, subtract = 7, then 7 < x < 17.

Question 32

What are the properties of parallelograms?

Answer 32

A parallelogram has 4 sides, and the total angles equal 360°.

Question 33

What are the properties of a rhombus?

Answer 33

A rhombus has all 4 sides equal, diagonals are perpendicular, and diagonals bisect opposite angles.

Question 34

What are the properties of a rectangle?

Answer 34

A rectangle has equal diagonals and four right angles (90°).

Question 35

What characterizes a square?

Answer 35

A square combines the properties of a rhombus and a rectangle.

Question 36

What are the properties of a kite?

Answer 36

A kite has equal opposite angles on the sides, diagonals are perpendicular, and the long diagonal bisects everything.

Question 37

What characterizes a trapezoid?

Answer 37

A trapezoid has only one pair of parallel sides, and same side angles sum to 180°.

Question 38

What does SOH CAH TOA stand for?

Answer 38

SOH: Sine = Opposite / Hypotenuse, CAH: Cosine = Adjacent / Hypotenuse, TOA: Tangent = Opposite / Adjacent

Question 39

What is the Angle of Elevation?

Answer 39

The angle formed by a horizontal line and the line of sight to an object above the horizontal.

Question 40

What is the Angle of Depression?

Answer 40

The angle formed by a horizontal line and the line of sight to an object below the horizontal.

Question 41

How do you find an angle using a calculator?

Answer 41

Hit 'Sin-1' (12/20) =

Question 42

What is the area formula for a square, rectangle, and parallelogram?

Answer 42

A = bh

Question 43

What is the area formula for a triangle?

Answer 43

A = 1/2 bh

Question 44

What is the area formula for a rhombus and kite?

Answer 44

A = 1/2 d1 * d2

Question 45

What is the area formula for a trapezoid?

Answer 45

A = 1/2 h(b1 + b2)

Question 46

What is the volume formula for prisms and cylinders?

Answer 46

V = Bh

Question 47

What is the volume formula for pyramids and cones?

Answer 47

V = 1/3 Bh

Question 48

What is the volume formula for spheres?

Answer 48

V = (4/3)πr^3

Question 49

What is the circumference formula for circles?

Answer 49

C = 2πr or C = πd

Question 50

What is the area formula for circles?

Answer 50

A = πr^2

Question 51

What is the arc length formula?

Answer 51

S = C * (m° / 360°)

Question 52

What is the area of a sector formula?

Answer 52

Asector = Acircle * (m° / 360°)

Question 53

How do you convert radians to degrees?

Answer 53

rad = (180/π) * degrees

Question 54

What is the equation of a circle?

Answer 54

(x - h)² + (y - k)² = r² ## Footnote (h,k) is the center of the circle; r is the radius.

Question 55

What is the formula for density?

Answer 55

Density = Mass / Volume

Question 56

What is population density?

Answer 56

Population Density = People / Area

Question 57

What is a centroid?

Answer 57

The point where the medians of a triangle meet, dividing each median in a 2:1 ratio.

Question 58

What is the relationship between central and inscribed angles?

Answer 58

Central Angle = Arc in degrees; Inscribed Angle = ½ of the Arc

Question 59

What is the relationship between an arc and an inscribed angle?

Answer 59

Arc = 2 times the inscribed angle

Question 60

What is the relationship between circumscribed angles and central angles?

Answer 60

Central angle + outside angle = 180°

Question 61

What is the relationship between opposite angles in quadrilaterals inside a circle?

Answer 61

Opposite angles = 180°