47
The triangle, its perimeter and kinds
Textbook, pp. 209–212
GoalKnow the triangle, its parts, perimeter and kinds; use the angle sum and the triangle inequality.
New words
triangle · uchburchakperimeter · perimetrisosceles triangle · teng yonli uchburchakhypotenuse · gipotenuza
Explanation
Joining three points that do not lie on one line with segments gives a triangle. The points are its vertices and the segments are its sides. Any side of a triangle is shorter than the sum of the other two sides. The sum of its angles is 180°. By angles a triangle is acute, right (the side opposite the right angle is the hypotenuse, the other two are legs) or obtuse. By sides it is scalene, isosceles (two equal sides) or equilateral. The perimeter is the sum of the three side lengths: P = AB + BC + AC.
Worked examples
Sides 7, 9, 12 cm: P = 7 + 9 + 12 = 28 cm. A triangle with sides 3, 4, 8 does not exist: 3 + 4 = 7 < 8.
If two angles are 55° and 75°, the third is 180° − 55° − 75° = 50°.
Class activity
“Stick triangles”: each pair gets sticks of different lengths (for example 3, 4, 8, 5, 6 cm). They find by experiment and by comparing sums which three sticks make a triangle.
Practice
1
Find the perimeter in cm of a triangle with sides 7 cm, 9 cm, 12 cm.
28
2
Two angles of a triangle are 55° and 75°. How many degrees is the third angle?
50
3
What kind of triangle by sides has sides 5, 5, 8?
Isosceles triangle
4
Why can a triangle not have two obtuse angles?
An obtuse angle is bigger than 90°; two of them would sum to more than 180°, but the angles of a triangle sum to exactly 180°.