Question

Given: m∠ABC = m∠CBD

Prove: BC bisects ∠ABD.

Justify the steps in the flowchart proof
a.
1)definition of congruent
2)definition of bisect
3)given
4)reflexive property
b.
1)definition of congruent
2)definition of bisect
3)given
4)reflexive property

c.
1)definition of congruent
2)definition of bisect
3)given
4)reflexive property

Answer 1

Answer:

(a) Option 3

(b) Option 1

(c) Option 2

Step-by-step explanation:

Given information: m∠ABC = m∠CBD

Prove: BC bisects ∠ABD.

Proof:

$m\angle ABC=m\angle CBD$             (Given)

Definition of congruent: Two angles are congruent if their measures are equal.

$\angle ABC\cong \angle CBD$         (Definition of bisect)

Definition of bisect: If a line divides an angle in two equal parts, then the line is called angle bisector.

BC bisects ∠ABD                    (Definition of bisect)

Hence proved.

Answer 2

An angle bisector divides the angle into two equal parts. The justification of each step of the flowchart is as follows

• Given
• Definition of congruent
• Definition of bisect

From the question, we are given that:

$\angle ABC =\angle CBD$

This represents the first step of the flowchart.

So, the justification is (3) Given

From the figure, we have that:

$\angle ABC \cong \angle CBD$

This represents the second step of the flowchart.

$\cong$ mean congruent

So, the justification is (1) Definition of congruent

Lastly:

Line BC bisects $\angle ABC$.

This represents the third step of the flowchart.

So, the justification is (2) Definition of bisect

Because line BC divides $\angle ABC$ into two equal halves.

Read more about bisections at:

https://brainly.com/question/2866798