Triangle Inequalities?

Question

Figure ABCD:
http://i13.tinypic.com/814d7nr.gif

1. The longest side of triangle ABC is

A. Segment AB
B. Segment BC
C. Segment AC

2. The shortest side of triangle ACD is

A. Segment AD
B. Segment CD
C. Segment AC

and

3. Triangle ABC with vertices A(-4,2), B(4,3), C(1,-3). list the angles in order from least measure to greatest measure.

thank you, thank you, thank you a million to anyone who helps!

Answer 1

1C
2B
3...Give me a minute...

Should be A, B, C...

(Check the sides; AB should be rad (sqr root) 65, BC should be rad 45 and AC should be rad 50. That gives you a relative measure of the angles; that is, the biggest side is opposite the biggest angle.)

Answer 2

PROBLEM 1:

The longest side will be opposite the longest angle.

Since the angles in a triangle add up to 180, the missing angle (
The largest angle is
Answer:
C) Segment AC

PROBLEM 2:

The missing angle is 37. The *shortest* side will be opposite the shortest angle, so that will be CD:

Answer:

B) Segment CD.

PROBLEM 3:

Use the distance formula for each pair of vertices.
Distance = sqrt((x2 - x1)² + (y2 - y1)²)

Length AB = sqrt((4 - (-4))² + (3 - 1)²)
Length AB = sqrt(8² + 4²)
Length AB = sqrt(64 +16) = sqrt(80)

Length BC = sqrt((4 - 1)² + (3 - (-3))²)
Length BC = sqrt(3² + 6²)
Length BC = sqrt(9 + 36) = sqrt(45)

Length AC = sqrt((1 - (-4))² + (-3 - 2)²)
Length AC = sqrt(5² + 5²)
Length AC = sqrt(50).

The sides in size order are: BC, AC, AB
Thus the *opposite* angles in order will be:

Answer 3

1. C. Segment AC. The longest side of a triangle will always be opposite of the largest angle. In this case angle B is the largest, so AC is the longest side.

2. B. Segment CD. The shortest side of a triangle will always be opposite of the smallest angle.

3. A, B, C

Answer 4

1. C because
the side opposite to the largest angle is the largest side.82 degrees is the largest angle of abc and the side opposite to it is AC.

2. B because

the side opposite to the smallest angle is the smallest side.

3. angle A, angle B, angle C is the order from least measure to greatest measure.

Answer 5

1C
2B
3CAB