## Math 6A, Lesson 14, Spring 2019, 6/2/2019

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1. Perpendicular Bisectors and Angle Bisectors

• Use of compass: center, radius, pin leg, and drawing leg
• To draw a circle
• To mark off or copy a line segment
• How to draw a perpendicular bisector of a line segment?
• Any point on the perpendicular bisector of a line segment is equidistant from the two  end points of the segment.

2. Angle Bisectors

• A ray AZ divides <BAC into two equal angles, <BAZ and <CAZ. The ray is called the angle bisector of <ABC
• How to draw an angle bisector?
• Any point on the angle bisector of an angle is equidistant from the two sides of the angle.

3. Class work

• Construct/draw circles, triangles, angles, equal line segments
• construct /draw perpendicular bisectors of line segments
• construct/draw angle bisectors of angles

4. Classification of Triangles

• The number of equal sides in the triangle: scalene triangle – no equal sides; isosceles triangle – two equal sides; equilateral triangles – three equal sides
• The type of angles of the triangle: acute-angled triangle – all angles are acute; right-angled triangle – one of the angles is a right angle; obtuse-angled triangle – one of the angles is an obtuse angle
• Is an equilateral triangle also an isosceles triangle?
• Is it Possible to draw a triangle with more than one obtuse angle?
• Can a scalene triangle be an acute-angled, right-angled or obtuse-angled triangle?
• All the three angles in a scalene triangle are different size
• The angles opposite the equal sides of an isosceles triangle are equal
• All the three angles in an equilateral triangle are equal in size

• A closed plane figure with four straight sides joined by four vertices is called a quadrilateral
• Vertices, diagonals
• Parallelogram: 2 pairs of parallel and equal opposite sides
• Rectangle: all angles are right angles
• Rhombus: all sides are equal, diagonals are perpendicular to each other
• Square: all sides are equal, all angles are right angles
• Trapezoid: 1 pair of parallel sides

6. Home Work:

• Handout:
• Two pages
• Workbook:
• Page 48-50: 12, 13, 14,15,16

## Math 6A, Lesson 13, Spring 2019, 5/19/2019

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2. Discount

• Discount = Marked price – Selling price
• Percentage discount = ( Discount / Marked_price) x 100%
• Selling price = (100% – Discount %) x Marked_price

3. Sales Tax and Income Tax

• Tax = Tax_rate x Cost
• Income_tax = Tax_rate x Income
• Income: wage (hourly-paid), salary (annual basis)

4. Compound Discount

• Each successive discount is based on the price after the previous discount

5. Points, Line and Planes

• Point: has position; has no size
• Line: has an infinite number of points; has no width; can be determined by two points; can be straight or curved
• Ray: a part of a line with one endpoint
• Endpoint
• Line segment: a part of a line between two end points; has length
• Plane: a flat surface; has no thickness
• Parallel lines: two lines on the same plane do not intersect (meet or cut)
• Perpendicular (lines) to each other: two lines intersect at right angle
• Foot of the perpendicular

6. Types of angles

• Acute angle: angle < 90 degree
• Right angle: angle = 90 degree
• Obtuse angle: 90 degree < angle < 180 degree
• Reflex angle: 180 degree < angle < 360 degree

7. Complementary, supplementary, and adjacent angles

• Complementary angles: the sum of two angles is 90 degree
• Supplementary angles: the sum of two angels is 180 degree
• Adjacent angles: two angles share a common side and a common vertex but do not overlap

8. Properties of Angles

• The sum of adjacent angles on a straight line is 180 degree
• The sum of all angles at a point is 360 degree
• Vertically opposite angles: when two lines intersect, the vertically opposite angles are equal

9. Home Work:

• Handout:
• Three pages
• Workbook:
• Page 45: 1, 2, 3
• Page 46: 4, 5

## Math 6A, Lesson 12, Spring 2019, 5/12/2019

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1. Reverse Percentage

• In a box, 15% of the balls are green. If there are 54 green balls, find the number of balls in the box.
• In the library, the fine for not returning a book on loan is 125% of the price of the book. If the fine for a book that was not returned was \$90, find the price of the book.

2. Percentage increase

• Increase = Increased_value ( End_value, or New_value) – Original_value
• Percentage increase = ( IncreaseOriginal_value) x 100%
• Increased_value = (100% + Increase %) x Original_value

3. Percentage decrease

• Decrease = Original_value – Decreased_value ( End_value, or New_value)
• Percentage decrease = (Decrease / Original_value) x 100%
• Decreased_value = (100% – Decrease %) x Original_value

4. Home Work:

• Handout:
• Three pages
• Workbook:
• Page 40: 8, 9, 10, 11

## Math 6A, Lesson 11, Spring 2019, 5/5/2019

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1. Percentage: a percentage is a fraction with 100 as the denominator

• Meaning of percentage: “per cent” means “by the hundred” or divided by one hundred. The term “percentage” is derived from the Latin per centum, meaning “per hundred”.

38% = 38/100 = 0.38

100% = 100/100 = 1

0% = 0/100 = 0

• Decimals, percentages and fractions and how to express a number in each form
• Express one quantity as a percentage of another
• Compare quantities using percentage
• Word problems involving percentage

2. Home Work:

• Handout:
• Two pages
• Workbook:
• Page 39: 1, 2, 3, 4, 5
• Page 40: 6, 7

## Math 6A, Lesson 10, Spring 2019, 4/28/2019

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Exam on ratio, rate, average rate, speed, uniform/constant speed and average speed, and Conversion of units.