Question

1. match the description to the most appropriate image. one is done for you.

word bank
a. angle bisector
b. supplementary angles
c. segment addition postulate
d. definition of midpoint
e. complementary angles

Explanation:

Step1: Analyze the first image (with \(3x\) and \(5x - 6\))

Since \(AB+BC = AC\) (by the Segment Addition Postulate), we have \(3x+(5x - 6)\). This is related to the Segment Addition Postulate which states that if \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\).

Step2: Analyze the second image (with \(m + 18\) and \(4m-2\))

Since \(AB + BC=AC\) (by the Segment Addition Postulate), we have \((m + 18)+(4m-2)\). This is related to the Segment Addition Postulate which states that if \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\).

Step3: Analyze the third image (right - angled at \(D\))

Complementary angles are two angles whose sum is \(90^{\circ}\). If \(\angle GDF+\angle FDE+\angle EDB = 90^{\circ}\), and we are dealing with angles that add up to a right - angle, we use the definition of complementary angles.

Step4: Analyze the fourth image (angle with \(26^{\circ}\) and \((5x + 11)^{\circ}\))

An angle bisector divides an angle into two equal parts. If the \(26^{\circ}\) angle and \((5x + 11)^{\circ}\) angle are created by an angle bisector, we use the definition of an angle bisector.

Answer:

First image: C. Segment Addition Postulate
Second image: C. Segment Addition Postulate
Third image: E. Complementary Angles
Fourth image: A. Angle bisector