Answer:
2/45
Step-by-step explanation:
0.04... is the same as 0.1 * 0.4... because we are moving it up a decimal place, it's the same as multiplying by ten: we needed to multiply by a tenth to cancel that out. 0.4... is the same as 4/9 and 0.1 is the same as 1/10. We can rewrite the expression above as: . Multiplying the two fractions results in 4/90 which can be simplified to 2/45.
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.
