## Math 7A, Lesson 16, Final Exam Fall 2021-2022, 1/23/2022

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The exam will cover all the materials we have learned in the Fall 2021-2022 term, namely chapters 3. 4. 5 & 8. See course info here.

The exam will be posted Saturday night in Google Classroom. Please print out all the pages before class.

## Math 7, Lesson 15, Fall 2021-2022, 1/16/2022

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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 7, Lesson 14, Fall 2021-2022, 1/9/2022

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## Chapter 8. Angles, triangles and quadrilaterials

#### 1. 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

#### 2. 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

#### 3. 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

#### 4. 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

#### 5. Home Work:

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