Section 1

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Supplementary angles

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Date created

Mar 14, 2020

Cards (95)

Section 1

(50 cards)

Supplementary angles

Front

angles whose sum is 180° (a straight line)

Back

Right Triangles and Pythagorean Thorem

Front

a & b = legs c = hypotenuse

Back

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?

Front

75 : 11

Back

Acute angle

Front

π‘₯° < 90°

Back

What are 'similar' triangles?

Front

Triangles with same angle measures but different side lengths.

Back

Right angle

Front

π‘₯° = 90°

Back

Q: √3 is approximately ___

Front

√3 ≈ 1.7

Back

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?

Front

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

Back

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

Front

SA = 90πœ‹

Back

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?

Front

2.592 kg

Back

Q: For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?

Front

4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

Back

Vertical angles

Front

Pairs of equal and opposite angles, formed by two lines intersecting.

Back

In any polygon, sum of all external angles = ___

Front

π“ͺ°+𝒃°+𝒄°+𝒅°+𝒆°=360°

Back

The ratio of the areas of two similar polygons is ...

Front

... the square of the ratios of the corresponding sides.

Back

sum of measure of angles in a triangle

Front

Back

What is a central angle?

Front

A central angle is an angle formed by 2 radii.

Back

What are 'congruent' triangles?

Front

Triangles with same angle measures and same side lengths.

Back

Q: A cylinder has surface area 22πœ‹. If the cylinder has a height of 10, what is its radius?

Front

π‘Ÿ = 1

Back

Perimeter of a Square (formula)

Front

P=4s

Back

Isosceles Triangle

Front

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

Back

The consecutive angles in a parallelogram equal = ___

Front

π“ͺ° + 𝒃² = 180°

Back

Q: A cylinder has a surface area of 22πœ‹. If the cylinder has a height of 10, what is the radius?

Front

π‘Ÿ = 1

Back

Complementary angles

Front

angles whose sum is 90° (a right angle)

Back

Q: The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?

Front

y=90°

Back

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

Front

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

Back

𝔁 : 𝔁 : 𝔁√2 is the ratio of the sides of what kind of triangle?

Front

π‘₯ : π‘₯ : π‘₯√2 is the ratio of a 45:45:90 isosceles right triangle.

Back

What is an exterior angle?

Front

Exterior angle 𝒅° = π“ͺ°+𝒃° 𝒅° + 𝒄° = 180° supplementary angles

Back

Q: √2 is approximately ___

Front

√2 ≈ 1.4

Back

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

Front

π‘₯ : π‘₯√3 : 2π‘₯ is the ratio of a 30 : 60 : 90 right triangle.

Back

Q: 𝝅 is approximately ___

Front

πœ‹ ≈ ²²⁄₇ or 3.14

Back

Q: √10 is approximately ___

Front

√10 ≈ 3.16

Back

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

Front

A° + B° + C°= 360° a° + b° + c°= 180°

Back

Perimeter of a figure

Front

Perimeter= sum of all sides

Back

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

Front

130πœ‹

Back

Q: Legs 5, 12. Hypotenuse?

Front

13

Back

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

Front

72

Back

Q: Legs 6, 8. Hypotenuse?

Front

10

Back

Obtuse angle

Front

90° < π‘₯° < 180°

Back

Special Right Triangles

Front

45°-45°-90° Isoceles-Right triangle 30°-60°-90° Right triangle

Back

Perimeter of a Rectangle (formula)

Front

P= 2𝓁 + 2𝑀

Back

Adjacent angles

Front

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

Back

Area of a triangle (formula)

Front

A= ½ × π‘ × ℎ (where 𝑏⊥ℎ) Area Right triangle= ½ × leg one (𝑏) × leg two (ℎ)

Back

Q: In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?

Front

4:5

Back

Q: Legs: 3 and 4. Hypotenuse?

Front

5

Back

What can you assume about measure of sides and angles of a random triangle?

Front

Sides π“ͺ, 𝒃, and 𝒄: 𝒃 + 𝒄 > π“ͺ > 𝒃 − 𝒄 Angles 𝑨°, 𝑩°, and π‘ͺ°: 𝑩° + π‘ͺ° > 𝑨° > 𝑩° − π‘ͺ° Longest side 𝒃 is opposite from largest angle 𝑩° Shortest side 𝒄 is opposite from smallest angle π‘ͺ°

Back

Equilateral Triangle

Front

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

Back

The sum of all angles around a point

Front

Back

Angle bisector

Front

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

Back

Straight angle

Front

π‘₯° = 180°

Back

Parallel lines cut by transversal

Front

π“ͺ°=𝒄°=𝐠°=𝒆° 𝒃°=𝒅°=𝐑°=𝙛°

Back

Section 2

(45 cards)

Quadrilateral: Parallelogram

Front

Back

How to answer questions containing complex figures?

Front

Break the figures down into simpler figures :)

Back

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

Front

Lateral surface area = 2πœ‹π‘Ÿℎ

Back

Arc Length (formula)

Front

Arc Length = (𝑛°/360°) × Circumference = (𝑛°/360°) × (πœ‹π‘‘)

Back

Area of a rectangle (formula)

Front

𝑨 rectangle = length × width

Back

A quadrilateral is a polygon with __ sides

Front

A quadrilateral is a polygon with 4 sides

Back

Quadrilateral: Trapezoid

Front

only two parallel sides

Back

Volume of a rectangular solid (formula)

Front

V = 𝓁 × π‘€ × ℎ

Back

Polygon

Front

A polygon is a closed figure whose sides are 3 or more straight line segments.

Back

A pentagon is a polygon with __ sides

Front

A pentagon is a polygon with 5 sides

Back

The sum of interior angles in a quadrilateral is ___

Front

= (#of sides−2) × 180° = (4 − 2) × 180° = 2 × 180° = 360°

Back

Area of a square (formula)

Front

𝑨 square = side²

Back

What is a chord of a circle?

Front

A chord is a line segment joining two points on a circle.

Back

Regular Polygon

Front

A regular polygon has sides of equal length and interior angles of equal measure.

Back

Sum of all interior angles of a polygon

Front

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

Back

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

Front

Surface Area = sum of areas of all faces Surface Area = 6𝑒³

Back

The sum of interior angles in a pentagon is ___

Front

= (#of sides−2) × 180° = (5 − 2) × 180° = 3 × 180° = 540°

Back

A hexagon is a polygon with __ sides

Front

A hexagon is a polygon with 6 sides

Back

Area of trapezoid (formula)

Front

𝑨 trapezoid = (average of parallel sides) × height = ½ × ( ⁄ ⁄ side₁ + ⁄ ⁄ sideβ‚‚) × height

Back

Volume of a cube (formula)

Front

V = side³

Back

If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle, the triangle is a ____ triangle

Front

AC = 𝑑 βˆ†ABC = right triangle

Back

45°-45°-90° Isoceles-Right triangle properties

Front

45° : 45° : 90° π‘₯ : π‘₯ : π‘₯√2

Back

The sum of interior angles in a hexagon is ___

Front

= (#of sides−2) × 180° = (6 − 2) × 180° = 4 × 180° = 720°

Back

Pythagorean triplets

Front

a : b : c 3 : 4 :5 5 :12 :13 8 :15 :17

Back

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

Front

𝑨 = ¼ × π‘²√3 𝒉 = ½ × π‘√3

Back

Area of a parallelogram (formula)

Front

𝑨 parallelogram = base × height

Back

Q: A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?

Front

13πœ‹ / 2

Back

Circle properties

Front

Diameter = 2 × Radius

Back

What is an arc of a circle?

Front

An arc is a portion of a circumference of a circle.

Back

Area of a circle (formula)

Front

𝑨 circle = πœ‹π‘Ÿ²

Back

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

Front

Surface Area = sum of areas of all faces Surface Area = 2 (𝓁𝑀 + 𝓁ℎ + 𝑀ℎ)

Back

Minor arc vs. Major arc

Front

Minor arc: shortest arc between points A and B on a circle's diameter. Major arc: longest arc between points A and B on a circle's diameter.

Back

Circumscribed figures

Front

Circumscribed means is outside of Circle is circumscribed about Square

Back

Inscribed figures

Front

Inscribed means is inside. Square is inscribed in Circle

Back

3D figures: face, edge, vertex

Front

This figure has 6 faces, 12 edges, 8 vertices

Back

30°-60°-90° Right triangle properties

Front

30° : 60° : 90° π‘₯ : π‘₯√3 : 2π‘₯

Back

Circumference of a circle (formula)

Front

π‘ͺircumference = 2πœ‹π‘Ÿ = πœ‹π‘‘

Back

Area of a sector of a circle (formula)

Front

Area of a Sector: = (𝑛°/360°) × (Area of Circle) = (𝑛°/360°) × (πœ‹π‘Ÿ²)

Back

𝝅 is a ratio of what to what?

Front

𝝅 = Circumference / Diameter

Back

Volume of a cylinder (formula)

Front

V = πœ‹π‘Ÿ²ℎ

Back

Quadrilateral: Square

Front

Back

The ratio of the Areas of two similar triangles

Front

Area βˆ†DEF / Area βˆ†ABC (DE)² / (AB)²

Back

What is a tangent?

Front

A tangent is a line that only touches one point on the circumference of a circle, and is perpendicular to the radius.

Back

Quadrilateral: Rectangle

Front

Back

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

Front

Total surface area = 2πœ‹π‘Ÿℎ + 2πœ‹π‘Ÿ²

Back