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klemol [59]
3 years ago
10

Rewrite each expression by factoring out the GCF:

Mathematics
1 answer:
mash [69]3 years ago
8 0
1. 7(2x+1)

2.3(3m-4)

3.-5(3y+5)

4.4(3b+5)
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Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals. Quadrilateral R
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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.

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1.4171428571428571428571428571429 milimeters per year or,

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