Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
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If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
Answer:
Given : ∠ABC is a right angle, ∠D BC is a straight angle.
To prove :∠AB D is a right angle.
Proof: ∠ ABC = 90°[ Given]
∠ D BC= 180° [ D BC is a straight line]
now, ∠ AB D and ∠ AB C are adjacent angles forming linear pair.
∠ AB D +∠ AB C =180° [By linear pair axiom]
⇒∠ AB D + 90= 180°
⇒∠ AB D=180°-90°
⇒∠ AB D=90°
∠AB D is a right angle
Hence proved.
The answer should be A because point slope form is y-y1=m(x-x1)....M is the starting point and its -56 and y1(-4) is the y value of the coordinate point and x1(8) is the x value of the coordinate point. it changes to y+4 because two negative signs make a positive(y--4)
