Question

Point B ∈ AC . If points K, M, N, and P are the midpoints of respectively AB , AC , MC , and NC , identify and write a statement about each pair of congruent segments.

Answer 1

AK ≅ KB

AM ≅ MC

MN ≅ NC

NP ≅ PC

Explanation:

Given that point K is the midpoint of AB, then by definition of midpoint:

AK ≅ KB

Given that point M is the midpoint of AC, then by definition of midpoint:

AM ≅ MC

Given that point N is the midpoint of MC, then by definition of midpoint:

MN ≅ NC

Given that point P is the midpoint of NC, then by definition of midpoint:

NP ≅ PC

Answer 2

AK and KB

AM and MC

MN and NC

NP and PC

Explanation:

* Lets explain how to solve the problem

- B ∈ AC

∴ B is located between A and C

- K is the mid point of AB

∴ K divides AB into two equal parts AK and KB

∴ AK = KB

- M is the mid point of AC

∴ M divides AC into two equal parts AM and MC

∴ AM = MC

- N is the mid point of MC

∴ N divides MC into two equal parts MN and NC

∴ MN = NC

- P is the mid point of NC

∴ P divides NC into two equal parts NP and PC

∴ NP = PC

* The congruent segments are:

AK and KB

AM and MC

MN and NC

NP and PC