Question

In Fig. 6.33, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB // CD.​

Answer 1

${\tt{Question}}\: \purple☟$

In Fig. 6.33, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB // CD.

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$\red&#9998{\tt{Answer}}\: \orange☟$

⠀⠀$&#9679\purple{\bf{See \:the \:attachment}}\red{⇑}$

⠀ $&#9679\orange{\bf{Question\: solved}}\: \green✔$

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All necessary formulas⤵️

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$\purple{\boxed{\bf{Angle\:sum\: property}}}$

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof .Thus, the sum of the interior angles of a triangle is 180°.

$\blue{\tt{Example:-}}$

$\red{\boxed{a+b+c=180°}}$

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$\orange{\boxed{\bf{Alternate\: interior\:angle}}}$

Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal.Alternate interior angles are equal if the lines intersected by the transversal are parallel.

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$\orange\star{\bf{\red{\underbrace{complementary \:angle}}}}\red\star$

The sum of 2 numbers$=90°$

example $a−b=90°$

how to find "a" if a is not mentioned

$\red{\underbrace{\bf{\orange{Given࿐}}}}$

$a= \: ?$

$b = 40$

$a+40=\:90°$

$a=90-40°$

$a=50°$

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$\pink\star{\bf{\purple{\underbrace{supplementary\: angle}}}}\red\star$

The sum of two numbers$= \:180°$

example $a+b=180°$

how to find "a" if a is not mentioned

Given

$a= \:?$

$b =\: 40$

$a+40=180°$

$a=180-40°$

$a=140°$

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$\orange\star{\bf{\green{\underbrace{Adjacent \:angle}}}}\red\star$

If there is a common ray between ${\bf&#x2220}a$ and ${\bf&#x2220}b$ so it is a adjacent angle.

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$\orange\star{\bf{\blue{\underbrace{Vertical\: opposite\: angle }}}}\red\star$

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

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$\orange\star{\bf{\orange{\underbrace{lenear\: pair \:of\: angles}}}}\red\star$

Here ${\bf&#x2220}a$$+{\bf&#x2220}b$$=$180°.

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Answer 2

In Fig. 6.33, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB // CD.

All necessary formulas⤵️

Angle sum property

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof .Thus, the sum of the interior angles of a triangle is 180°.

Example:−

a+b+c=180°

a+b+c=180°

Alternat einterior angle

Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal.Alternate interior angles are equal if the lines intersected by the transversal are parallel.

comple mentary angle

The sum of 2 numbers=90°=90°=90°

example

Given

a=?a= \: ?a=?

b=40b = 40b=40

a+40=90°a+40=\:90°a+40=90°

a=90−40°a=90-40°a=90−40°

a=50°a=50°a=50°

supple mentary angle

The sum of two numbers=180°= \:180°=180°

example a+b=180°a+b=180°a+b=180°

how to find "a" if a is not mentioned

Given

a=?a= \:?a=?

b=40b =\: 40b=40

a+40=180°a+40=180°a+40=180°

a=180−40°a=180-40°a=180−40°

a=140°a=140°a=140°

Adjacent angle

If there is a common ray between ∠a{\bf∠}a∠a and ∠b{\bf∠}b∠b so it is a adjacent angle.

Vertical opposite angle

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

lenear pair of angles

Here ∠a{\bf∠}a∠a +∠b+{\bf∠}b+∠b === 180°.