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Alenkinab [10]
3 years ago
6

Given: M ≅ X N ≅ Y YO ≅ NZ Prove: △MNO ≅ △XYZ

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
6 0

Answer:

Δ MNO ≅ ΔXYZ ⇒ proved down

Step-by-step explanation:

Cases of congruency

  • SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ  
  • SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ  
  • ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ  
  • AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ  
  • HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ  

Let us solve the question using the 4th rule above

∵ YZ = YO + OZ

∵ NO = NZ + ZO

∵ OZ = ZO ⇒ from the figure

∵ YO ≅ NZ ⇒ given

∴ YZ ≅ NO

In Δs MNO and XYZ

∵ ∠M ≅ ∠X ⇒ given

∵ ∠N ≅ ∠Y ⇒ given

∵ NO ≅ YZ ⇒ proved

→ By using the AAS postulate of congruency.

∴ Δ MNO ≅ ΔXYZ  

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Paul needs to buy paint to cover all outside surfaces of his shed, depicted below. How much area, in square yards, does he need
Alekssandra [29.7K]

Answer:

Area = 145.7 Square yards

Step-by-step explanation:

Since there is no picture attached to depict the house and its dimension, I am taking values of a similar problem.

<em><u>Dimensions of Shed</u></em>

2 walls with dimensions of 15 ½ ft. by 12 ft.

2 walls with dimensions of 25 ¼ ft. by 12 ft.

Ceiling with dimensions of 15 ½ ft. by 25 ¼ ft.

2 windows that are each 2 ft. by 4½ ft. as well as an 8-ft. by 5-ft. door

<u>Solution</u>

We need to find the total wall area and ceiling area which when combined will give us the total area shed's outer surface that needs to be painted.

For total area of the wall, we need to first find the sum of area for each wall and subtract area of windows and door

Wall Area = Area of 1st two walls+Area of other two walls-Area of 2 windows-Area of door=[15.5(12)(2)] + (25.25) (12) (2) - (2)(2) (4.5) -(8)(5)

Wall Area = 371 + 606 - 17 - 40

Wall Area = 920 square ft = 102.2 square yards

Ceiling Area is just the area of the ceiling

Ceiling Area = (15.5) (25.25 )

Ceiling Area = 391.375 square ft= 43.486 square yard

<u>Total Area = Wall Area+Ceiling Area </u>=102.2+43.486=145.7 Square yards

Which is the area paul needs to cover with paint.

<em>Note: Converted Square foot to square yard as the problem requires that.</em>

8 0
4 years ago
8 ft 6 inches is greater or less than 100 inches?
Romashka [77]
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3 years ago
Brilliance for the right answer
maks197457 [2]
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3 years ago
Read 2 more answers
What is 0.353 rounded to the nearest tenth
KengaRu [80]
0.4 .

Explanation
Rounding to the tenth, you look at the 2nd number after the period, if it’s greater than 5 or 5 itself u and 1 to the first number after the period. Back to the question 0.353 , the 2nd number after the period is 5, so u add 1 to the 1st number after the period with it’s 3 and 3+1=4. If you are rounding to tenth only leave one number after the period with gives you 0.4. Hopefully you get it.
4 0
2 years ago
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