Chapter 2: Q11 (page 40)

Copy everything shown and supply missing statements and reasons.
Given:
$m ∠ 1 = m ∠ 3$ ;
$m ∠ 2 = m ∠ 4$
Prove: $m ∠ A B C = m ∠ D E F$
Proof:

Short Answer

Expert verified

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

$m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 4$

Step by step solution

Step 1. Apply the addition property of algebra.

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

$m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 4$

Step 2. Angle addition postulate.

From the given figure, it can be observed that some of $m ∠ 1$ and $m ∠ 2$ gives $m ∠ A B C$ , that is $m ∠ 1 + m ∠ 2 = m ∠ A B C$ .

From the given figure, it can be observed that some of $m ∠ 3$ and $m ∠ 4$ gives $m ∠ D E F$ , that is $m ∠ 3 + m ∠ 4 = m ∠ D E F$ .

Step 3. Apply substitution property.

Substitute $m ∠ A B C$ for $m ∠ 1 + m ∠ 2$ and $m ∠ D E F$ for $m ∠ 3 + m ∠ 4$ in step 1.

$\begin{matrix} m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 4 \\ m ∠ A B C = m ∠ D E F \end{matrix}$

Hence, it is proved that $m ∠ A B C = m ∠ D E F$ .

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Copy everything shown and supply missing statements and reasons.
Given:
$m ∠ 1 = m ∠ 3$ ;
$m ∠ 2 = m ∠ 4$
Prove: $m ∠ A B C = m ∠ D E F$
Proof:

Short Answer

Step by step solution

Step 1. Apply the addition property of algebra.

Step 2. Angle addition postulate.

Step 3. Apply substitution property.

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Copy everything shown and supply missing statements and reasons.Given:m∠1=m∠3;m∠2=m∠4Prove: m∠ABC=m∠DEFProof:

Short Answer

Step by step solution

Step 1. Apply the addition property of algebra.

Step 2. Angle addition postulate.

Step 3. Apply substitution property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Applied Mathematics

Mechanics Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Copy everything shown and supply missing statements and reasons.
Given:
$m ∠ 1 = m ∠ 3$ ;
$m ∠ 2 = m ∠ 4$
Prove: $m ∠ A B C = m ∠ D E F$
Proof: