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Chapter III review
Textbook: pp. 70–72
GoalReview the Chapter III notions and congruence criteria.
New words
congruence criteria · tenglik alomatlariisosceles triangle · teng yonli uchburchakmedian · medianaperpendicular bisector · o‘rta perpendikulyar
Explanation
Review: a polygon is a closed broken line without self-crossing. Congruence criteria: SAS (two sides and the included angle), ASA (a side and its two adjacent angles), SSS (three sides). In an isosceles triangle the base angles are equal; the bisector to the base is both median and altitude. Points of the perpendicular bisector are equidistant from the ends of the segment. In a proof: write what is given and what is to be proved, find equal triangles, name the criterion, then conclude that corresponding elements are equal.
Worked examples
AO = OC, BO = OD (O is where AC and BD meet). SAS: △AOB = △COD ⇒ AB = CD.
△ABC is isosceles, AB = AC = 13, BC = 10; the median AM to the base. Then BM = 5 and AM ⊥ BC.
Class activity
“Name the criterion”: cards list equal elements; teams quickly say whether it is SAS, ASA or SSS.
Practice
1
The median to the base 22 cm of an isosceles triangle cuts it into two parts; how long is one (cm)?
11
2
△ABC = △DEF (SSS), ∠A = 41°. Find ∠D (degrees).
41
3
Isosceles triangle with perimeter 50 cm and legs 18 cm. Find the base (cm).
14
4
Which criterion is used when two sides and the angle between them are equal?
SAS