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stira [4]
3 years ago
10

The congruence theorem that can be used to prove ALON

Mathematics
1 answer:
Arisa [49]3 years ago
3 0

Answer:

SSS is the congruence theorem that can be used to prove Δ LON  is congruent to Δ LMN ⇒ 1st answer

Step-by-step explanation:

Let us revise the cases of congruence

  • 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 leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ  

In triangles LON and LMN

∵ LO ≅ LM ⇒ given

∵ NO ≅ NM ⇒ given

∵ LN is a common side in the two triangles

- That means the 3 sides of Δ LON are congruent to the 3 sides

   of Δ LMN

∴ Δ LON ≅ LMN ⇒ by using SSS theorem of congruence

SSS is the congruence theorem that can be used to prove Δ LON  is congruent to Δ LMN

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Step-by-step explanation:

Solve algebraically using a system of equations

Assign variables

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<u>Rearrange the equation for people</u>. Isolate the variable you don't want to find.

a = 541 - c

<u>Substitute</u> "541 - c", replacing "a", in the equation for money

2.25a + 1.75c = 1041.25              

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1217.25 - 0.5c = 1041.25                   Simplified equation

<u>Start isolating "c".</u> Move anything that's not "c" to the right side. Move numbers in reverse BEDMAS order. That means we will add/subtract before dividng/multiplying. When moving a number, do its reverse operation to the entire equation.

1217.25 - 0.5c = 1041.25      Do the reverse of positive 1217.25

1217.25 - 1217.25 - 0.5c = 1041.25 - 1217.25    Subtract 1217.25 on both sides  

-0.5c = -176               Do the reverse of multiplying by -0.5

-0.5c/-0.5 = -176/-0.5               Divide both sides by -0.5

c = 352                Number of children

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