Chapter 2: Q13 (page 52)

Complete.
$∠ F O B ≅ \underline{?}$

Short Answer

Expert verified

The complete statement is: $∠ F O B ≅ ∠ E O C$ .

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Definition of congruent angles.

The two angles are said to be congruent angles if they have equal measure.

If two angles A and B are congruent then it can be written as $∠ A ≅ ∠ B$ .

Step 3. Write the theorem 2-3.

Theorem 2-3 states that the vertical angles are congruent.

Step 4. Write the relations between the angles FOB and EOC.

From the diagram, it can be noticed that:

The angles $F O B$ and $E O C$ are vertically opposite angles.

Therefore, from theorem 2-3, it can be said that the angles $F O B$ and $E O C$ are congruent angles.

Step 5. Complete the statement.

As the angles $F O B$ and $E O C$ are congruent angles.

Therefore, $∠ F O B ≅ ∠ E O C$ .

Therefore, the complete statement is: $∠ F O B ≅ ∠ E O C$ .

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Statement	Reasons
1. A, M, and B have coordinated a, x, and b respectively; $b > a$ .	1. ?
2. $A M = x - a; M B = b - x$	2. ?
3. M is the midpoint of $\bar{A B}$ .	3. ?
4. $\bar{A M} ≅ \bar{M B}$ , or $A M = M B$	4. ?
5. $x - a = b - x$	5. ?
6. $2 x =$ ?	6. ?
7. $x = \frac{a + b}{2}$	7. ?

Statement	Reasons
1. $\vec{B X}$ is the bisector of $∠ A B C$	1. ?
2. $∠ A B X ≅$ ?, or $m ∠ A B X =$ ?	2. ?
3. $m ∠ A B X + m ∠ X B C = m ∠ A B C$	3. ?
4. $m ∠ A B X + m ∠ A B X = m ∠ A B C$ , or $2 m ∠ A B X = m ∠ A B C$	4. ?
5. $m ∠ A B X = \frac{1}{2} m ∠ A B C$	5. ?
6. $m ∠ X B C = \frac{1}{2} m ∠ A B C$	6. Substitution Prop. (Steps ? and ?)

Complete.
$∠ F O B ≅ \underline{?}$

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Definition of congruent angles.

Step 3. Write the theorem 2-3.

Step 4. Write the relations between the angles FOB and EOC.

Step 5. Complete the statement.

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Complete.∠FOB≅?¯

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Definition of congruent angles.

Step 3. Write the theorem 2-3.

Step 4. Write the relations between the angles FOB and EOC.

Step 5. Complete the statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Complete.
$∠ F O B ≅ \underline{?}$