Write the fraction in lowest terms 45 over 55
2 answers:
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<u><em>Answer:</em></u>
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<u><em>Explanation:</em></u>
<u>Before we begin, remember the following rules:</u>
<u>1- Distribution property:</u>
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<u>2- Simplification of fractions:</u>
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<u>3- Signs in multiplication:</u>
+ve * +ve = +ve
-ve * -ve = +ve
+ve * -ve = -ve
<u>Now, for the given problem, we have:</u>
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<u>Starting with the distributive property:</u>
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..................>This corresponds to option 1
<u>Now, we simplify the output from the above step:</u>
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................> This corresponds to option 5
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We have to prove that rectangles are parallelograms with congruent Diagonals.
Solution:
1. ∠R=∠E=∠C=∠T=90°
2. ER= CT, EC ║RT
3. Diagonals E T and C R are drawn.
4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]
5. Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]
6. In Δ ERT and Δ CTR
(a) ER= CT→→[Opposite sides of parallelogram]
(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]
(c) Side TR is Common.
So, Δ ERT ≅ Δ CTR→→[SAS]
Diagonal ET= Diagonal CR →→→[CPCTC]
In step 6, while proving Δ E RT ≅ Δ CTR, we have used
(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]
Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.
