46
Chapter V review
Textbook: pp. 116–118
GoalReview the Chapter V relations between triangle sides and angles.
New words
angle sum · burchaklar yig‘indisiexterior angle · tashqi burchakhypotenuse · gipotenuzatriangle inequality · uchburchak tengsizligi
Explanation
Review: the interior angles of a triangle sum to 180°; an exterior angle equals the sum of the two non-adjacent interior angles. In a right triangle the acute angles sum to 90°, the leg opposite 30° is half the hypotenuse and the median to the hypotenuse is half of it; congruence criteria are LL, LA, HA, HL. A point on an angle bisector is equidistant from the sides. The larger side lies opposite the larger angle. Any side of a triangle is less than the sum and greater than the difference of the other two. When solving, draw a figure, list the known properties and check your answer.
Worked examples
There is no triangle with sides 2, 3 and 5 cm: 2 + 3 = 5, which is not strictly greater.
In △ABC with ∠A = 30°, ∠C = 90°, AB = 16: BC = 8 (opposite 30°) and ∠B = 60°.
Class activity
“Chapter V quiz”: teams answer six questions; 1 point for each correct answer.
Practice
1
Two angles of a triangle are 48° and 67°. Find the third (degrees).
65
2
In a right triangle the leg opposite 30° is 9 cm. Find the hypotenuse (cm).
18
3
Two sides are 7 and 10; the third is a whole number. How many values are possible?
13
4
Why is the hypotenuse longer than a leg?
It lies opposite the right angle, legs lie opposite acute angles; the larger angle has the larger side.