20
The triangle and its types
Textbook: pp. 54–55
GoalKnow the triangle, its elements and types.
New words
triangle · uchburchakperimeter · perimetrisosceles · teng yonliequilateral · teng tomonli
Explanation
A figure made of three points not on one line and the three segments joining them in pairs is called a triangle, written △ABC. The points are vertices, the segments are sides, and ∠A, ∠B, ∠C are its angles. Sides and angles are its main elements. The sum of the three sides is the perimeter: P = AB + BC + AC. By sides: equilateral (all three equal), isosceles (two equal), scalene. By angles: right (one angle 90°), acute (all angles acute), obtuse (one obtuse angle). We say “∠BAC lies between sides AB and AC” and “side BC lies opposite ∠A”.
Worked examples
Isosceles △ABC: AB = BC = 5 cm, AC = 8 cm. P = 5 + 5 + 8 = 18 cm.
An isosceles triangle has perimeter 26 cm and its base is 4 cm shorter than a leg: leg x, base x − 4; 3x − 4 = 26, x = 10; sides 10, 10, 6 cm.
Class activity
“Triangle types”: build triangles from straws or sticks and name each type (use sticks under adult supervision).
Practice
1
An equilateral triangle has side 9 cm. Find its perimeter (cm).
27
2
An isosceles triangle has legs 12 and base 7 cm. Find the perimeter (cm).
31
3
An isosceles triangle with perimeter 40 cm has base 10 cm. Find a leg (cm).
15
4
Why is an equilateral triangle also isosceles?
It has two equal sides (in fact all three are equal).