ASAP HELP!! In triangles DEF and OPQ, ∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ. Is this information sufficient to prove triangles DEF and OPQ congruent through SAS? Explain your answer.

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I THINK they are congruent because you said "∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ."

Step-by-step explanation:

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No this information is not sufficient to prove triangles DEF and OPQ are congruent through SAS because this information doesn't provide another pair of congruent sides in order to be SAS. Another reason this information is inefficient, they provided two pairs of congruent angles rather than two congruent sides and one congruent angle.  This information provided shows angles DEF and OPQ being congruent through ASA rather than SAS. There are two angles that are congruent, provided by the information above, and both angles are set on a congruent side making it ASA.

Step-by-step explanation:

DEF and OPQ

Angle D =Angle O —Angle

Line DF = Line OQ—Side

Angle F= Angle Q—Angle

The information provided shows DEF and OPQ through ASA rather than SAS. Therefore, the following information is not sufficient to prove DEF and OPQ through SAS.

(Below is not the answer just saying if they wanted to prove DEF and OPQ through SAS it would be this)

—If they wanted to prove it through SAS the information should have stated:

DEF and OPQ

Line EF is congruent to Line PQ—Side

Angle F is congruent to Angle Q—Angle

Line DF is congruent to Line OQ—Side 

Making triangle DEF and OPQ congruent through SAS. 

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step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;