Question

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

Answer 1

Based on the diagram below showing the construction of the bisector of ∠ABC, a statement that is not true is: 3) m∠EBF = m∠ ABC

In Mathematics and Euclidean Geometry, an angle bisector is a type of line, ray, or segment, that typically divides or bisects a line segment exactly into two (2) equal and congruent angles.

Based on the definition of angle bisector, we can logically deduce the following angle measures;

m∠EBF = 1/2 × m∠ABC.

m∠DBF= 1/2 × m∠ABC

m∠DBF = m∠EBF

Complete Question:

The diagram below shows the construction of the bisector of ∠ABC. Which statement is not true?

1) m∠EBF= 1/2 m∠ ABC

2) m∠ DBF= 1/2 m∠ ABC

3) m∠ EBF=m∠ ABC

4) m∠ DBF=m∠ EBF

Answer 2

`c)\overline{AC}=2\overline{AB}`

Explanation:

Retrieved Information:

Which statement is not true?

a)
`a)\overline{AC}=\overline{CB}\\b)\overline{CB}=(1)/(2)\overline{AB} \\c)\overline{AC}=2\overline{AB}\\d)\overline{AC}+\overline{CB}=\overline{AB}`

b) Check the graph below

1) To bisect is to equally divide an angle or a line segment, into two equal parts. The bisector of AC divides the line segment AC in its midpoint, so AC≅CB, therefore AC=CB. In addition to this, this is equivalent to say that CB is = 1/2AB.

Finally, this is also true that AC+CB=AB.

2) Clearly AC is not equal to 2AB since AC=CB is = 1/2AB then it is false.

`c)\overline{AC}=2\overline{AB}\:FALSE`