35
Review problems
Textbook: Part 1, lesson 35, pp. 134–135
GoalReview angles, parallel and perpendicular lines, broken lines and perimeter.
New words
angle · burchakbisector · bissektrisaperpendicular · perpendikulyarperimeter · perimetr
Explanation
Angles are measured in degrees with a protractor: acute is less than 90°, right is 90°, obtuse is greater than 90° and less than 180°, straight is 180°. A bisector divides an angle in half. The angles of a triangle add up to 180°. For two intersecting lines vertical angles are equal and all four angles add up to 360°. Parallel lines do not intersect; perpendicular lines meet at 90°. The length of a broken line and the perimeter of a polygon equal the sum of the side lengths; for a rectangle P = 2(a + b), for a square P = 4a.
Worked examples
If two intersecting lines form a 40° angle, the others are 140°, 40°, 140°; the sum is 40 + 140 + 40 + 140 = 360.
A rectangle with sides 18 m and 31 m has perimeter 2(18 + 31) = 98 m. The bisector of an 86° angle splits it into two angles of 43°.
Class activity
“Geometry relay”: teams quickly complete a card task (naming an angle type, bisector, perimeter) and pass it to the next team member.
Practice
1
Find the angle made by the bisector of an 86° angle.
43
2
Two angles of a triangle are 48° and 73°. Find the third.
59
3
Find the perimeter (m) of a rectangle with sides 18 m and 31 m.
98
4
Which is obtuse: 38°, 90°, 127° or 180°? Why?
127°: it is greater than 90° and less than 180°.