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Chapter 2: Q3 (page 46)

State which definition, postulate, or theorem justifies the statement about the diagram.

If AD→ bisects ∠BAC, then ∠1≅∠2 .

Short Answer

Expert verified

The angle bisector theorem justifies the statement about the diagram.

Step by step solution

01

Step 1. Observe the given diagram.

The diagram constitutes of a triangle ABC and AD→ bisects ∠BAC.

02

Step 2. State the angle bisector theorem.

The theorem states that if a line bisects an angle of a triangle, then that line divides the opposite side of that angle into two segments proportional to other two sides of the triangle.

03

Step 3. State the conclusion.

Considering the given diagram and the statement: “if AD→bisects ∠BAC, then ∠1≅∠2.

Therefore, the statement about the diagram is justified by the angle bisector theorem.

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Most popular questions from this chapter

Provide a counterexample to show that each statement is false.

Statement: If a four-sided figure has four congruent sides, then it has four right angles.

Mention what can be deduced from the given information.

Given: AC¯bisects DB¯

DB¯bisects AC¯

CE=BE

Write a definition of a right angle as a biconditional.

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a line lies in a vertical plane, then the line is vertical.

Copy everything shown and write a two-column proof.

Given:m∠SRT=m∠STR;

m∠3=m∠4

Proof:m∠1=m∠2
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