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The law of cosines is used for this purpose. It tells you
c² = a² + b² - 2ab×cos(C)
Solving for the angle C gives
C = arccos((a² + b² - c²)/(2ab))
C = arccos(( 17² + 15² - 19²)/(2×17×15))
C = arccos(153/510)
C ≈ 72.5424°
The measure of the angle opposite the longest side is about 73°.
Answer:
1. a, b, d, e
2. c. Triangles ABE and BAD are congruent
d. Triangles AED and BDE are congruent
Step-by-step explanation:
1. Trapezoid is a quadrilateral which has two parallel opposite sides. Isosceles trapezoid has congruent legs.
Consider all options:
a. Sides AE and BD are congruent (by definition of isosceles trapezoid) - true
b. Sides AB and ED are parallel (by definition of trapezoid) - true
c. AB is not congruent to ED (AB and ED are trapezoid's bases, they are never congruent) - false
d. AE is congruent to BD as legs of isosceles trapezoid - true
e. AB is parallel to ED as bases of trapezoid - true
2. Consider all options:
a. Triangles ABE and DBE are not congruent (ABE is obtuse triangle, DBE is acute triangle)
b. Triangles ABD and DAE are not congruent (ABD is obtuse triangle, DAE is acute triangle)
c. Triangles ABE and BAD are congruent by SAS postulate
d. Triangles AED and BDE are congruent by SAS postulate
e. Triangles EAB and EDB are not congruent (EAB is obtuse triangle, EDB is acute triangle)
Negative, positive, positive, positive, positive
The answer to this is -20
