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Grade 8 review

Lessons 49 · 1 lessons · A. A. Rahimqoriyev, M. A. To‘xtaxo‘jayeva. Geometry, Grade 8 (textbook for general secondary schools), revised 3rd edition. Yangiyo‘l Poligraf Servis, Tashkent, 2014
49

Review of the Grade 8 topics

Textbook: pp. 152–153
GoalReview the main topics of Grade 8 geometry.
New words
Pythagorean theorem · Pifagor teoremasiarea of a trapezoid · trapetsiya yuziinscribed angle · ichki chizilgan burchakvector · vektor
Explanation

Review: the interior angles of a quadrilateral add up to 360°, and of an n-gon to (n − 2) · 180°. Areas: parallelogram S = a · h, triangle S = ½ a h, rhombus S = d₁ d₂ : 2, trapezoid S = (a + b) : 2 · h. In a right triangle c² = a² + b² (the Pythagorean theorem); the area from the three sides is found with Heron’s formula. In a circle an inscribed angle is half its arc, and one on a diameter is 90°; a tangent is perpendicular to the radius, and tangent segments from an outside point are equal. A vector is determined by modulus and direction, sums use the triangle or parallelogram rule, and operations in coordinates act on corresponding coordinates.

Worked examples
An isosceles trapezoid has bases 6 and 14 and legs 5. Half the difference of the bases is 4, the altitude is 3 and the area is 10 · 3 = 30.
In a circle of radius 10 a chord is 12: the distance from the centre is √(100 − 36) = 8.
Class activity

“Year quiz”: in teams, write one question on each chapter (quadrilaterals, area, Pythagoras, circle, vectors) and pass it to another team.

Practice
1
What is the sum of the interior angles of a convex octagon (degrees)?
2
A triangle has base 14 and altitude 9. What is its area?
3
What is the modulus of the vector →a(5; 12)?
4
Why is an inscribed angle subtending a diameter equal to 90°?