Tell whether the triangles are similar. Explain.
2 answers:
Answer:
Step-by-step explanation:
We can use the AA Similarity Theorem that says that if two corresponding pairs of angles are congruent then the two triangles are similar.
11.
On the big triangles we are given one angle is 90° , one angle is 51° and
we know that the sum of all angles in a triangle is 180.
Calculate the missing angle in the big triangle:
180 -90-51 = 39°
Also in the picture we see a given angle of 102° that is adjacent to the 39° angle and another missing angle adjacent that form together 180° given the 2 triangles sin on a straight line.
Calculate the third missing angle
180 -39-102 = 39°
The green triangles are similar because of AA Similarity Theorem.
A= 39°=39° angles with same measure are congruent
A=90°=90° all right angles are congruent
12.
We have 2 vertical angles here and we know that vertical angles are congruent. Is given one of the vertical angle is 29° so the other vertical angle is 29° as well.
We are also given an angle of 88° and given that the sum of angles in a Δ is 180° we can find the third angle in that Δ.
180-29-88 = 63°
On the Δ that is on the right side we are given an angle of 91° and an adjacent angle along a straight line so they must form together 180°. 91+89 = 180
So the third angle in the Δ is 180-29-89 = 62.
We can see here that the angles are not congruent so the yellow triangles are NOT similar.
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Answer:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis:
Alternative hypothesis:
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
Step-by-step explanation:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis:
Alternative hypothesis:
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
And the data given from the sample is:
represent the sample mean
represent the population deviation
represent the sample size
And the statistic would be given by: