geometry flashcards.pdf
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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
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