Question

use this diagram for items 5 - 8.

1. write a statement from the diagram that can be justified by using the angle addition postulate.
2. write a statement from the diagram that can be justified by using the definition of a right angle.
3. given that ( k ) is the midpoint of ( fj ), write a statement that can be justified by using the definition of a midpoint.
4. given that ( angle ghf cong angle jfh ), write a statement that can be justified by using the definition of congruent angles.

Explanation:

Item 5

Step1: Recall Angle Addition Postulate

The Angle Addition Postulate states that if a point \( K \) lies in the interior of \( \angle GFJ \), then \( m\angle GFK + m\angle KFJ = m\angle GFJ \). From the diagram, \( K \) is on \( FJ \), so \( \angle GFJ \) is composed of \( \angle GFK \) and \( \angle KFJ \).

Step2: Formulate the statement

Using the Angle Addition Postulate, we can say that \( m\angle GFJ = m\angle GFK + m\angle KFJ \) (or \( \angle GFJ=\angle GFK + \angle KFJ \) in terms of angle composition).

Step1: Recall the definition of a right angle

A right angle is an angle whose measure is \( 90^\circ \). In the diagram, \( \angle GFK \) (or \( \angle GFJ \) if \( GK \) is perpendicular to \( FJ \)) appears to be a right angle (since \( GF \) and \( GK \) seem perpendicular, forming a right angle at \( F \) or \( K \)).

Step2: Formulate the statement

Using the definition of a right angle, we can say that \( m\angle GFK = 90^\circ \) (meaning \( \angle GFK \) is a right angle).

Step1: Recall the definition of a midpoint

The definition of a midpoint states that if \( K \) is the midpoint of \( FJ \), then \( FK = KJ \) (and \( FK=\frac{1}{2}FJ \), \( KJ = \frac{1}{2}FJ \)).

Step2: Formulate the statement

Using the definition of a midpoint, we can say that \( FK = KJ \) (or \( FK=\frac{1}{2}FJ \), \( KJ=\frac{1}{2}FJ \)).

Answer:

\( m\angle GFJ = m\angle GFK + m\angle KFJ \) (or \( \angle GFJ=\angle GFK + \angle KFJ \))

Item 6