☰ Contents · Geometry

Review of Grade 7

Lessons 1 · 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
1

Review of Grade 7 material

Textbook: pp. 3–6
GoalRecall adjacent and vertical angles, the main lines of a triangle, the congruence tests and the angle sum.
New words
adjacent angles · qo‘shni burchaklarvertical angles · vertikal burchaklarmedian, bisector, altitude · mediana, bissektrisa, balandlikexterior angle · tashqi burchak
Explanation

Grade 8 geometry builds on Grade 7, so we recall the key facts. Adjacent angles add up to 180°, and vertical angles are equal. A median joins a vertex to the midpoint of the opposite side, a bisector halves an angle, and an altitude is the perpendicular from a vertex to the opposite side. The interior angles of a triangle add up to 180°, and an exterior angle equals the sum of the two interior angles not adjacent to it. There are three congruence tests: two sides and the included angle; one side and the two angles next to it; all three sides.

Worked examples
Two lines intersect and the adjacent angles are in the ratio 2 : 7. 2x + 7x = 180°, x = 20°, so the angles are 40° and 140°.
In triangle ABC, ∠A = 47° and the exterior angle at C is 112°. The exterior angle equals ∠A + ∠B, so ∠B = 112° − 47° = 65°. Then ∠C = 180° − 47° − 65° = 68°.
Class activity

“Quick quiz”: the teacher asks short questions about angles and triangles, teams answer in turn and get 1 point for each correct answer.

Practice
1
Two lines intersect and one angle is 64°. How many degrees is an adjacent angle?
2
Two angles of a triangle are 58° and 77°. How many degrees is the third angle?
3
The interior angles at A and B of a triangle are 40° and 65°. How many degrees is the exterior angle at C?
4
Why can adjacent angles not be 100° and 90°?