The sum of all angles around a point

1a

1b

Right angle

2a

° = 90°

2b

Acute angle

3a

° < 90°

3b

Obtuse angle

4a

90° < ° < 180°

4b

Straight angle

5a

° = 180°

5b

Adjacent angles

6a

Any angles that share a common side and acommon vertex. Angle 1 and Angle 2 are adjacent

angles. 6b

Vertical angles

7a

Pairs of equal and opposite angles, formedby two lines intersecting.

7b

Supplementary angles

8a

angles whose sum is 180° (a straight line)

8b

Complementary angles

9a

angles whose sum is 90° (a right angle)

9b

Angle bisector

10a

a ray from a vertex of an angle that dividesthe angle into two angles of equal measure.

10b

Parallel lines cut by transversal

11a

°= °= °= °°= °= °= °

11b

sum of measure of angles in a triangle

12a

12b

Area of a triangle (formula)

13a

A= ½ × × ℎ (where ⊥ℎ)Area Right triangle= ½ × leg one ( ) × leg two

(ℎ) 13b

Q: What is the side length of an equilateraltriangle with height 6?

14a

4√3. The triangle can be divided into twoequal 30-60-90 triangles with side 6 as the

side in which 6 = √3. So =2√3

14b

Perimeter of a Rectangle (formula)

15a

P= 2 + 2

15b

In any polygon, sum of all externalangles = ___

16a

°+ °+ °+ °+ °=360°

16b

The consecutive angles in aparallelogram equal = ___

17a

° + ² = 180°

17b

Perimeter of a Square (formula)

18a

P=4s

18b

What is a central angle?

19a

A central angle is an angle formed by 2radii.

19b

Q: Legs: 3 and 4. Hypotenuse?

20a

5

20b

Q: Legs 6, 8. Hypotenuse?

21a

10

21b

Q: Legs 5, 12. Hypotenuse?

22a

13

22b

Q: The four angles around a point measurey, 2y, 35 and 55 respectively. What is the

value of y?

23a

y=90°

23b

Q: For similar triangles, the ratio of theircorresponding sides is 2:3. What is the ratio

of their areas?

24a

4:9. The ratio of the areas of two similartriangles equals the square of the ratio of the

corresponding sides.

24b

: : √2 is the ratio of the sidesof what kind of triangle?

25a

: : √2 is the ratio of a 45:45:90 isosceles right triangle.

25b

: √3 : 2 is the ratio of the sidesof what kind of triangle?

26a

: √3 : 2 is the ratio of a 30 : 60 : 90 right triangle.

26b

Q: In a triangle where the two legs are 4 and3, what is the value of a line directlyintersecting the middle coming from themeeting point of the two legs?

27a

2.4. We calculate the area (6) and then turnthe triangle on its side and use x as theheight to calculate again. (5x)/2=6

27b

Q: What is the measure of an exterior angleof a regular pentagon?

28a

72

28b

The ratio of the areas of two similarpolygons is ...

29a

... the square of the ratios of thecorresponding sides.

29b

Q: In similar hexagons, the ratio of theareas is 16:25. What is the ratio of their

corresponding sides?

30a

4:5

30b

Q: A cylinder has a surface area of 22 . Ifthe cylinder has a height of 10, what is the

radius?

31a

= 1

31b

Q: Find the surface area of a cylinder withradius 3 and height 12.

32a

SA = 90

32b

Q: What is the surface area of a cylinderwith radius 5 and height 8?

33a

130

33b

Q: A cylinder has surface area 22 . If thecylinder has a height of 10, what is its

radius?

34a

= 1

34b

Q: What is the ratio of the surface area of acube with an edge of 10 to the surface area ofa rectangular solid with dimensions 2, 4,and 6?

35a

75 : 11

35b

Q: A brick with dimensions 10, 15 and 25weighs 1.5 kg. A second brick (same density)has dimensions 12, 18, and 30. What is theweight of the second brick?

36a

2.592 kg

36b

Equilateral Triangle

37a

All three *sides are equal* and all three*angles are 60°*

37b

What are 'congruent' triangles?

38a

Triangles with same angle measures andsame side lengths.

38b

What are 'similar' triangles?

39a

Triangles with same angle measures butdifferent side lengths.

39b

Isosceles Triangle

40a

Two sides (legs) are equal and have thesame base angles.

40b

Q: √2 is approximately ___

41a

√2 ≈ 1.4

41b

Q: √3 is approximately ___

42a

√3 ≈ 1.7

42b

Q: √10 is approximately ___

43a

√10 ≈ 3.16

43b

Q: is approximately ___

44a

≈ ²²⁄₇ or 3.14

44b

What can you assume about measureof sides and angles of a random

triangle?

45a

Sides , , and : + > > −

Angles °, °, and °:° + ° > ° > ° − °

Longest side is opposite from largest angle °Shortest side is opposite from smallest angle ° 45b

Perimeter of a figure

46a

Perimeter= sum of all sides

46b

In a triangle: what is the sum of theexterior angles? And the sum of the

interior angles?

47a

A° + B° + C°= 360°a° + b° + c°= 180°

47b

What is an exterior angle?

48a

Exterior angle ° = °+ °° + ° = 180° supplementary angles

48b

Right Triangles and PythagoreanThorem

49a

a & b = legsc = hypotenuse

49b

Special Right Triangles

50a

45°-45°-90° Isoceles-Right triangle

30°-60°-90° Right triangle

50b

45°-45°-90° Isoceles-Right triangleproperties

51a

45° : 45° : 90° : : √2

51b

30°-60°-90° Right triangle properties

52a

30° : 60° : 90° : √3 : 2

52b

Pythagorean triplets

53a

a : b : c3 : 4 :5

5 :12 :138 :15 :17

53b

The ratio of the Areas of two similartriangles

54a

Area ∆DEF / Area ∆ABC(DE)² / (AB)²

54b

Polygon

55a

A polygon is a closed figure whose sides are3 or more straight line segments.

55b

Regular Polygon

56a

A regular polygon has sides of equal lengthand interior angles of equal measure.

56b

A quadrilateral is a polygon with __sides

57a

A quadrilateral is a polygon with 4 sides

57b

A pentagon is a polygon with __ sides

58a

A pentagon is a polygon with 5 sides

58b

A hexagon is a polygon with __ sides

59a

A hexagon is a polygon with 6 sides

59b

Sum of all interior angles of a polygon

60a

sum interior angles° of a polygon:= (#of sides−2) × 180°

= (#of ∆ in figure) × 180°

60b

The sum of interior angles in aquadrilateral is ___

61a

= (#of sides−2) × 180°= (4 − 2) × 180°

= 2 × 180°= 360°

61b

Quadrilateral: Square

62a

62b

Quadrilateral: Rectangle

63a

63b

Quadrilateral: Parallelogram

64a

64b

Quadrilateral: Trapezoid

65a

only two parallel sides

65b

The sum of interior angles in apentagon is ___

66a

= (#of sides−2) × 180°= (5 − 2) × 180°

= 3 × 180°= 540°

66b

The sum of interior angles in ahexagon is ___

67a

= (#of sides−2) × 180°= (6 − 2) × 180°

= 4 × 180°= 720°

67b

Area of a rectangle (formula)

68a

rectangle = length × width

68b

Area of a parallelogram (formula)

69a

parallelogram = base × height

69b

Area of trapezoid (formula)

70a

trapezoid = (average of parallel sides) × height

= ½ × ( ⁄ ⁄ side₁ + ⁄ ⁄ side₂) × height

70b

Circle properties

71a

Diameter = 2 × Radius

71b

Area of a circle (formula)

72a

circle = ²

72b

Circumference of a circle (formula)

73a

ircumference = 2 =

73b

is a ratio of what to what?

74a

= Circumference / Diameter

74b

What is a chord of a circle?

75a

A chord is a line segment joining two pointson a circle.

75b

What is an arc of a circle?

76a

An arc is a portion of a circumference of acircle.

76b

Minor arc vs. Major arc

77a

Minor arc: *shortest arc* between points A and B on a circle'sdiameter.

Major arc: *longest arc* between points A and B on a circle'sdiameter. 77b

Arc Length (formula)

78a

Arc Length= ( °/360°) × Circumference

= ( °/360°) × ( )

78b

Area of a sector of a circle (formula)

79a

Area of a Sector:= ( °/360°) × (Area of Circle)

= ( °/360°) × ( ²)

79b

What is a tangent?

80a

A tangent is a line that only touches one point onthe circumference of a circle, and is perpendicular

to the radius. 80b

Area of a square (formula)

81a

square = side²

81b

Q: A triangle is inscribed in a semi circlewith legs 5 and 12. What is the

circumfermence of the semicircle?

82a

13 / 2

82b

Inscribed figures

83a

Inscribed means is inside.Square is inscribed in Circle

83b

Circumscribed figures

84a

Circumscribed means is outside ofCircle is circumscribed about Square

84b

If a triangle is inscribed in a circle sothat one of its sides is a diameter ofthe circle, the triangle is a ____triangle

85a

AC = ∆ABC = right triangle

85b

3D figures: face, edge, vertex

86a

This figure has 6 faces, 12 edges, 8 vertices

86b

Surface Area of a 3D figure:Rectangular solid (formula)

87a

Surface Area = sum of areas of all facesSurface Area = 2 ( + ℎ + ℎ)

87b

Surface Area of a 3D figure: Cube(formula)

88a

Surface Area = sum of areas of all facesSurface Area = 6 ³

88b

Lateral surface area of a 3D figure:Cylinder (formula)

89a

Lateral surface area = 2 ℎ

89b

Total surface area of a 3D figure:Cylinder (formula)

90a

Total surface area = 2 ℎ + 2 ²

90b

Volume of a cylinder (formula)

91a

V = ²ℎ

91b

Volume of a rectangular solid (formula)

92a

V = × × ℎ

92b

Volume of a cube (formula)

93a

V = side³

93b

How to answer questions containingcomplex figures?

94a

Break the figures down into simpler figures:)

94b

Equilateral triangle: Area (formula)and height (formula)

95a

= ¼ × ²√3 = ½ × √3

95b