Question

Help pls for BRAINLIEST! From each given statement below, select the definition, property, postulate, or theorem that justifies each prove statement.

Answer 1

The definition, property, postulate, or theorem that justifies each statement are given as follows:

5. C. Whole Greater Than Its Part Property.

6. B. Exterior Angle Inequality Theorem.

7. E. If Unequal Sides, then Unequal Angles.

What justifies statement 5?

Segment AD is given by the combination of segments AM and MD, hence it's length is given by:

AD = AM + MD.

Segment length's are never negative nor zero, hence:

• AD > AM.

• AD > MD.

Thus statement C is correct.

C. Whole Greater Than Its Part Property.

What justifies statement 6?

The exterior angle inequality theorem states that the measure of any of the exterior angles of a triangle is greater than either of the opposite angles, hence:

• m<DMG > m>A.

• m<DMG > m>G.

Thus statement B is correct.

B. Exterior Angle Inequality Theorem.

What justifies statement 7?

We are given that the length of segment AM is less than the length of segment AG.

Applying the law of sines, we have that:

$\frac{AM}{\sin{G}} = \frac{AG}{\sin{M}}$

Hence:

$AG = AM\frac{\sin{M}}{\sin{G}}$

Since AG < AM, sin(M) < sin(G) and m<AGM < m<AMG. This is used to explain statement E, as follows:

E. If Unequal Sides, then Unequal Angles.

More can be learned about trigonometric postulates at brainly.com/question/24133971

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