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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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Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and
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Answer:

The quadratic equation used to determine the thickness of frame is \left(3+2x\right)\times \left(2+2x\right)=7

Step-by-step explanation:

Refer to the attachment for the diagram.

Consider EFGH as the the frame and ABCD as the mirror which is to be hanged.

Let me the "x" be the thickness of the frame as shown in diagram.

Given that, BC = 3 ft and DC = 2 ft which is the dimensions of the mirror.

Now to calculate the length and width of the frame consider following calculation,

Width of frame HG = x + DC + x  

Width of frame HG = x + 2 + x  

Width of frame HG =  2 + 2x  

2x is the addition of the thickness which is present on both side of mirror

Length of frame FG = x + BC + x

Length of frame FG = x + 3 + x

Length of frame FG = 3 + 2x

Since it is an rectangular frame, so using the formula for area of rectangle

Area\:of\:rectangle = length \times width

Given that area of frame is 7\:ft^{2}

Substituting the value,

7 = \left(3+2x\right)\times \left(2+2x\right)

Therefore, the quadratic equation used to determine the thickness of frame is \left(3+2x\right)\times \left(2+2x\right)=7

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