Question

(1) If DF = FB, then point F is called the _____ and segments DF and FB are _____.

a. bisector, collinear
b. congruent, midpoint
c. midpoint, congruent
d. midpoint, coplanar

(2) If ray FA bisects angle EFB and measure of angle EFA = 47 degrees, the measure of angle EFB = _____.

a. 94
b. 23.5
c. 47

(3) If seg DF = x+2, seg FB = 2x+1 and DB = 15, find the value of x.

(4) Based on your answer in #3 and the lengths for DF and FB after x is found, F is the midpoint of seg DB. True or False?

Answer 1

(1) C

(2) C

(3) 4

(4) False

Explanation:

(1) If DF = FB, then point F is called the midpoint and segments DF and FB are congruent.

(2) If ray FA bisects angle EFB, then angles EFA and AFB are congruent. If measure of angle EFA = 47 degrees, the measure of angle EFB = 47 degrees.

(3) If DF = x+2, FB = 2x+1 and DB = 15, then

DF + FB = DB

x+2+2x+1=15

3x+3=15

3x=15-3

3x=12

x=4

(4) If x=4, then

DF=4+2=6

FB=2·4+1=9

Since DF is not congruent to FB, F is not a midpoint. False