Chapter 6: Q21. (page 212)

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.
If $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

Short Answer

Expert verified

Hence proved that if $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

Step by step solution

Step 1. Define contrapositive statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

The given statement is if $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if $m ∠ D + m ∠ C = 180 °$ then $m ∠ A + m ∠ B = 180 °$ .

Step 3. Prove the statement

Since the sum of all angles of a quadrilateral is 360, therefore following will hold from the given figure as:

$\begin{matrix} m ∠ A + m ∠ B + m ∠ D + m ∠ C = 360 ° \\ m ∠ A + m ∠ B + 180^{o} = 360 ° \\ m ∠ A + m ∠ B = 360 ° - 180 ° \\ m ∠ A + m ∠ B = 180 ° \end{matrix}$

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Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.
If $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .

Short Answer

Step by step solution

Step 1. Define contrapositive statement

Step 2. Let the given statement and find its contrapositive

Step 3. Prove the statement

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Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.If m∠A+m∠B≠180°then m∠D+m∠C≠180°.

Short Answer

Step by step solution

Step 1. Define contrapositive statement

Step 2. Let the given statement and find its contrapositive

Step 3. Prove the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Pure Maths

Logic and Functions

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.
If $m ∠ A + m ∠ B \neq 180 °$ then $m ∠ D + m ∠ C \neq 180 °$ .