Chapter 2: Q8 (page 41)

Copy everything shown and supply missing statements and reasons.
Given: $F L = A T$
Prove: $F A = L T$
Proof:

Short Answer

Expert verified

By reflexive property, $L A = L A$ .

Step by step solution

Step 1. Apply the reflexive property of congruence.

By reflexive property, $L A = L A$ .

Step 2. Addition property of algebra.

If $a = b$ and $c = d$ , then $a + c = b + d$ .

Step 3. Description of step.

Use given information and step 1 and apply the addition property of algebra mentioned in step 2.

$F L + L A = A T + L A$

Step 4. Apply segment addition postulate.

From the given figure, it can be observed that some of $F L$ and $L A$ gives $F A$ and the sum of $L A$ and $A T$ gives $L T$ , that is,

$\begin{matrix} F L + L A = F A; \\ L A + A T = L T \end{matrix}$

Step 5. Substitution property.

Substitute $F A$ for $F L + L A$ and $L T$ for $L A + A T$ into step 3.

$\begin{matrix} F L + L A = A T + L A \\ F A = L T \end{matrix}$

Hence, it is proved that $F A = L T$ .

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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 ?)

Copy everything shown and supply missing statements and reasons.
Given: $F L = A T$
Prove: $F A = L T$
Proof:

Short Answer

Step by step solution

Step 1. Apply the reflexive property of congruence.

Step 2. Addition property of algebra.

Step 3. Description of step.

Step 4. Apply segment addition postulate.

Step 5. Substitution property.

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Copy everything shown and supply missing statements and reasons.Given:FL=ATProve: FA=LTProof:

Short Answer

Step by step solution

Step 1. Apply the reflexive property of congruence.

Step 2. Addition property of algebra.

Step 3. Description of step.

Step 4. Apply segment addition postulate.

Step 5. Substitution property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Copy everything shown and supply missing statements and reasons.
Given: $F L = A T$
Prove: $F A = L T$
Proof: