Section 1
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Supplementary angles
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Last updated
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Date created
Mar 14, 2020
Cards (95)
Section 1
(50 cards)
Supplementary angles
angles whose sum is 180° (a straight line)
Right Triangles and Pythagorean Thorem
a & b = legs c = hypotenuse
Q: What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2, 4, and 6?
75 : 11
Acute angle
π₯° < 90°
What are 'similar' triangles?
Triangles with same angle measures but different side lengths.
Right angle
π₯° = 90°
Q: √3 is approximately ___
√3 ≈ 1.7
Q: In a triangle where the two legs are 4 and 3, what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
Q: Find the surface area of a cylinder with radius 3 and height 12.
SA = 90π
Q: A brick with dimensions 10, 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12, 18, and 30. What is the weight of the second brick?
2.592 kg
Q: For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Vertical angles
Pairs of equal and opposite angles, formed by two lines intersecting.
In any polygon, sum of all external angles = ___
πͺ°+π°+π°+π °+π°=360°
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
sum of measure of angles in a triangle
What is a central angle?
A central angle is an angle formed by 2 radii.
What are 'congruent' triangles?
Triangles with same angle measures and same side lengths.
Q: A cylinder has surface area 22π. If the cylinder has a height of 10, what is its radius?
π = 1
Perimeter of a Square (formula)
P=4s
Isosceles Triangle
Two sides (legs) are equal and have the same base angles.
The consecutive angles in a parallelogram equal = ___
πͺ° + π² = 180°
Q: A cylinder has a surface area of 22π. If the cylinder has a height of 10, what is the radius?
π = 1
Complementary angles
angles whose sum is 90° (a right angle)
Q: The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
y=90°
Q: What is the side length of an equilateral triangle with height 6?
4√3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = π₯√3. So π₯ =2√3
π : π : π√2 is the ratio of the sides of what kind of triangle?
π₯ : π₯ : π₯√2 is the ratio of a 45:45:90 isosceles right triangle.
What is an exterior angle?
Exterior angle π ° = πͺ°+π° π ° + π° = 180° supplementary angles
Q: √2 is approximately ___
√2 ≈ 1.4
π : π√3 : 2π is the ratio of the sides of what kind of triangle?
π₯ : π₯√3 : 2π₯ is the ratio of a 30 : 60 : 90 right triangle.
Q: π is approximately ___
π ≈ ²²⁄β or 3.14
Q: √10 is approximately ___
√10 ≈ 3.16
In a triangle: what is the sum of the exterior angles? And the sum of the interior angles?
A° + B° + C°= 360° a° + b° + c°= 180°
Perimeter of a figure
Perimeter= sum of all sides
Q: What is the surface area of a cylinder with radius 5 and height 8?
130π
Q: Legs 5, 12. Hypotenuse?
13
Q: What is the measure of an exterior angle of a regular pentagon?
72
Q: Legs 6, 8. Hypotenuse?
10
Obtuse angle
90° < π₯° < 180°
Special Right Triangles
45°-45°-90° Isoceles-Right triangle 30°-60°-90° Right triangle
Perimeter of a Rectangle (formula)
P= 2π + 2π€
Adjacent angles
Any angles that share a common side and a common vertex. Angle 1 and Angle 2 are adjacent angles.
Area of a triangle (formula)
A= ½ × π × ℎ (where π⊥ℎ) Area Right triangle= ½ × leg one (π) × leg two (ℎ)
Q: In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
Q: Legs: 3 and 4. Hypotenuse?
5
What can you assume about measure of sides and angles of a random triangle?
Sides πͺ, π, and π: π + π > πͺ > π − π Angles π¨°, π©°, and πͺ°: π©° + πͺ° > π¨° > π©° − πͺ° Longest side π is opposite from largest angle π©° Shortest side π is opposite from smallest angle πͺ°
Equilateral Triangle
All three sides are equal and all three angles are 60°
The sum of all angles around a point
Angle bisector
a ray from a vertex of an angle that divides the angle into two angles of equal measure.
Straight angle
π₯° = 180°
Parallel lines cut by transversal
πͺ°=π°=π °=π° π°=π °=π‘°=π°
Section 2
(45 cards)