53
Problem solving
Textbook: pp. 136–137
GoalApply methods for solving construction problems.
New words
construction plan · yasash rejasitwo sides and an angle · ikki tomon va burchakright triangle · to‘g‘ri burchakli uchburchakverification · tekshirish
Explanation
In a construction problem first find what is given and what must be built, then make a plan: build the main parts one after another, justify each step and check the result at the end. A triangle from two sides and the included angle: construct the angle, lay the given segments on its sides and join the ends (SAS). A right triangle from its legs: construct perpendicular lines and lay the legs on them (LL). An isosceles triangle from its base and a leg needs three sides (SSS). To construct a triangle equal to a given one, copy its corresponding sides and angles.
Worked examples
AB = 5 cm, AC = 6 cm, ∠A = 40°: construct the angle, lay AB and AC, join B and C — by SAS the triangle is unique.
A right triangle with legs 3 and 4 cm: measuring the hypotenuse on the drawing gives 5 cm, so the perimeter is 3 + 4 + 5 = 12 cm.
Class activity
“Write a plan”: groups write a construction plan for a triangle from two sides and an angle; another group carries it out.
Practice
1
How many different triangles exist with sides 6 and 8 cm and included angle 50° (up to equality)?
1
2
A right triangle with legs 6 and 8 cm was built; the hypotenuse is 10 cm. Perimeter (cm)?
24
3
An isosceles triangle with base 8 cm and legs 5 cm has perimeter (cm)?
18
4
Why verify after the construction?
To make sure the figure meets the conditions and to find errors.