18
Chapter II review
Textbook: pp. 44–45
GoalReview the Chapter II material on angles.
New words
types of angles · burchak turlariadjacent angles · qo‘shni burchaklarbisector · bissektrisaperpendicular · perpendikulyar
Explanation
Review: an angle is two rays from one point; a straight angle is 180°; acute < 90°, right = 90°, obtuse between 90° and 180°. The bisector halves an angle. Adjacent angles add to 180° and vertical angles are equal. A theorem has a hypothesis and a conclusion and may be proved by contradiction. Perpendicular lines meet at 90°; the distance from a point to a line is the length of the perpendicular. In angle problems draw a figure, call the unknown x and write an equation; check the answer, e.g. whether a sum equals 180°.
Worked examples
Two lines intersect; one angle is 4x and its adjacent angle is 2x: 6x = 180°, x = 30°; the angles are 120° and 60°.
OC bisects ∠AOB = 130°, OD bisects ∠AOC: ∠AOC = 65°, ∠AOD = 32.5°.
Class activity
“Angle relay”: teams take turns solving an angle problem on the board, 1 point for each correct answer.
Practice
1
Adjacent angles are 3x and 6x. Find x (degrees).
20
2
Two lines intersect and an angle is 38°. Find an adjacent angle (degrees).
142
3
The bisector of ∠AOB = 76° makes two angles; what is their sum (degrees)?
76
4
Why does the bisector of a right angle make angles of 45°?
The bisector halves the angle: 90° : 2 = 45°.