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Review tasks and problems
Textbook: pp. 150–153
GoalReview the main definitions and theorems of Grade 7 geometry.
New words
axiom · aksiomatheorem · teorematriangle inequality · uchburchak tengsizligiparallel lines · parallel to‘g‘ri chiziqlar
Explanation
In the review we connect the main topics. Adjacent angles sum to 180°, vertical angles are equal. Triangle congruence criteria: SAS, ASA, SSS. The base angles of an isosceles triangle are equal. The angles of a triangle sum to 180°, and an exterior angle equals the sum of the two non-adjacent angles. A transversal of parallel lines makes equal corresponding angles. Each side of a triangle is less than the sum of the other two. Constructions use only compass and straightedge. In every problem remember the four stages.
Worked examples
A transversal crosses two parallel lines; one of the co-interior angles is 110°. These angles sum to 180°, so the other is 180° − 110° = 70°.
Prove each angle of an equilateral triangle is 60°: since the sides are equal, every pair of angles is equal (isosceles property), so all three angles are equal; 180° : 3 = 60°.
Class activity
Write topic names on a sheet and add one theorem or formula to each: make a “topic map”.
Practice
1
Two angles of a triangle are 35° and 75°. How many degrees is the third?
70
2
An exterior angle is 125° and one non-adjacent angle is 80°. How many degrees is the other?
45
3
An isosceles triangle has legs 9 cm and base 4 cm. What is its perimeter in cm?
22
4
Why does no triangle with sides 3, 4 and 8 cm exist?
Because 3 + 4 = 7, which is less than 8; the triangle inequality fails.