☰ Contents · Geometry

Construction problems and Chapter VI review

Lessons 53–54 · 2 lessons · Geometry Grade 7, corrected and expanded 3rd edition. Yangiyo‘l Poligraf Servis, Tashkent, 2017 (approved by the Ministry of Public Education)
54

Chapter VI review

Textbook: pp. 138–139
GoalReview the construction methods of Chapter VI.
New words
construction · yasashbisector · bissektrisaperpendicular bisector · o‘rta perpendikulyarconstructing a triangle · uchburchak yasash
Explanation

Review: constructions with compass and straightedge use only the allowed operations. Copying an angle onto a ray relies on SSS; the bisector is found by intersecting equal circles centred at points on the sides. A perpendicular and the midpoint of a segment are built with equal circles centred at the endpoints. A triangle is built from three sides (if a + b > c), from two sides and the included angle, or from a side and two adjacent angles. In every construction: plan, carry out, justify, verify.

Worked examples
Bisect an angle and bisect the result again: 100° → 50° → 25°.
A triangle with sides 5, 12, 13 exists: 5 + 12 > 13.
Class activity

“Construction quiz”: a card names a construction (bisector, perpendicular, midpoint); the team recites the steps in order.

Practice
1
Bisecting a 160° angle twice gives how many degrees?
2
C is the midpoint of AB = 26. AC = ?
3
Can a triangle with sides 4, 6, 9 cm be built?
4
Which criterion justifies the bisector construction and why?