GIVEN ∠ABC ≅ ∠DEF ∠GHI ≅ ∠DEF m∠ABC=m∠GHI
1 answer:
By the substitution property of equality, measure of ∠ABC ≅ measure of ∠GHI (m∠ABC=m∠GHI)
<h3>Substitution property of equality</h3>The <em>substitution property of equality</em> states that if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation
From the given information, we have that
∠ABC ≅ ∠DEF
and
∠GHI ≅ ∠DEF
By the substitution property, ∠ABC can be substituted for ∠DEF in the second equation
That is,
∠GHI ≅ ∠ABC
∴ ∠ABC ≅ ∠GHI
Hence, measure of ∠ABC ≅ measure of ∠GHI (m∠ABC=m∠GHI)
Learn more on Substitution property of equality here: brainly.com/question/2279838
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Answer:
Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.
Step-by-step explanation:
Let us assume the time taken by Dwight to split a cord of firewood = K hrs
So, the per hour rate of Dwight =
As, Joe uses 3 LESS hours then Dwight.
So, the time taken by Joe to split a cord of firewood = (K- 3) hrs
So, the per hour rate of Joe =
Now, when both of them wok together, it takes them 2 hours.
So, the per hour rate of BOTH of them =
⇒ Per hour rate of ( Dwight + Joe) =
Now, solving for the value of K , we get:
Implies either K = 6 Or K = 1
But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.
⇒ K = 6 hours
Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.