Chapter 2: Q11 (page 42)

Copy everything shown and write a two-column proof.
Given: $m ∠ 1 = m ∠ 2;$
$m ∠ 3 = m ∠ 4;$
Prove: $m ∠ S R T = m ∠ S T R$

Short Answer

Expert verified

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

$m ∠ 1 + m ∠ 3 = m ∠ 2 + m ∠ 4$

Step by step solution

Step 1. Apply the addition property of algebra.

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

$m ∠ 1 + m ∠ 3 = m ∠ 2 + m ∠ 4$

Step 2. Angle addition postulate.

From the given figure, it can be observed that some of $m ∠ 1$ and $m ∠ 3$ gives $m ∠ S R T$ , that is $m ∠ 2 + m ∠ 4 = m ∠ S T R$ .

From the given figure, it can be observed that some of $m ∠ 2$ and $m ∠ 4$ gives $m ∠ S T R$ , that is $m ∠ 2 + m ∠ 4 = m ∠ S T R$ .

Step 3. Apply substitution property.

Substitute $m ∠ S R T$ for $m ∠ 1 + m ∠ 3$ and $m ∠ S T R$ for $m ∠ 2 + m ∠ 4$ in step 1.

$\begin{matrix} m ∠ 1 + m ∠ 3 = m ∠ 2 + m ∠ 4 \\ m ∠ S R T = m ∠ S T R \end{matrix}$

Step 4. Write a two-column proof.

Write a two-column proof with the help of the above-mentioned steps.

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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 write a two-column proof.
Given: $m ∠ 1 = m ∠ 2;$
$m ∠ 3 = m ∠ 4;$
Prove: $m ∠ S R T = m ∠ S T R$

Short Answer

Step by step solution

Step 1. Apply the addition property of algebra.

Step 2. Angle addition postulate.

Step 3. Apply substitution property.

Step 4. Write a two-column proof.

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Copy everything shown and write a two-column proof.Given:m∠1=m∠2;m∠3=m∠4;Prove:m∠SRT=m∠STR

Short Answer

Step by step solution

Step 1. Apply the addition property of algebra.

Step 2. Angle addition postulate.

Step 3. Apply substitution property.

Step 4. Write a two-column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Copy everything shown and write a two-column proof.
Given: $m ∠ 1 = m ∠ 2;$
$m ∠ 3 = m ∠ 4;$
Prove: $m ∠ S R T = m ∠ S T R$