Question

1. point m is the mid - point of line segment ab. find bm.

a. 32
b. 9
c. 42
d. 84

1. the diagram to the right shows the construction of the bisector of ∠abc. which statement below is not true?

a. m∠ebf = 1/2m∠abc
b. m∠dbf = 1/2m∠abc
c. m∠ebf = m∠abc
d. m∠ebf = m∠dbf

1. what is the meaning of the symbol ≅?

a. congruent
b. approximately
c. similar
d. equal

1. find the measure of angle b.

a. 27°
b. 63°
c. 153°
d. 180°

1. which equation can be used to find the value of x?

a. 10x - 5 = 4x + 3
b. 10x - 5+4x + 3 = 90
c. 10x - 5+4x + 3 = 180
d. 10x - 5 = 180

1. which equation can be used to find the value of x?

a. x - 6+9 = 2x - 19
b. 47 = x - 6+9+2x - 19
c. 2x - 19+9 = 47
d. x + 3 - 47 = 2x - 19

Explanation:

Step1: Analyze question 4

Since M is the mid - point of AB, AM = MB. But the lengths are not given in the problem description, so we can't solve this part without more information. Skipping to other questions.

Step2: Analyze question 5

An angle bisector divides an angle into two equal parts. So if BF is the bisector of ∠ABC, then m∠EBF=m∠DBF and m∠EBF = 1/2m∠ABC and m∠DBF=1/2m∠ABC. The statement m∠EBF = m∠ABC is not true.

Step3: Analyze question 6

The symbol ≅ means congruent.

Step4: Analyze question 7

If two lines intersect, vertical angles are equal. If the angle opposite to b is 27°, then b = 27° because vertical angles are congruent.

Step5: Analyze question 8

The angles (10x - 5) and (4x + 3) are supplementary (they form a straight - line, so their sum is 180°). The equation to find x is 10x−5 + 4x+3 = 180.

Step6: Analyze question 9

The sum of the lengths of the segments on the line NK is equal to the length of NK. So (x - 6)+9+(2x - 19)=47, which simplifies to x−6 + 9+2x−19 = 47.

Answer:

1. C. m∠EBF = m∠ABC
2. A. Congruent
3. A. 27°
4. C. 10x−5 + 4x+3 = 180
5. B. 47=x−6 + 9+2x−19