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3 years ago

Which theorem or postulate proves that △ABC and △DEF are similar?

Mathematics

1 answer:

omeli [17]3 years ago

6 0

Answer:

The triangles are similar by AA Similarity Postulate

Step-by-step explanation:

we know that

In the triangle ABC

m∠CAB=65°

m∠ABC=m∠CAB

m∠ABC=65°

<em>Find the measure of angle ACB</em>

Remember that

The sum of the internal angles in a triangle must be equal to 180 degrees

m∠ACB+m∠ABC+m∠CAB=180°

substitute the values

m∠ACB+65°+65°=180°

m∠ACB=180°-130°=50°

In the triangle DEF

m∠FDE=m∠CAB=65°

m∠DFE=50°

<em>Find the measure of angle DEF</em>

Remember that

The sum of the internal angles in a triangle must be equal to 180 degrees

m∠DEF+m∠FDE+m∠DFE=180°

substitute the values

m∠DEF+65°+50°=180°

m∠DEF=180°-115°=65°

therefore

m∠CAB=m∠FDE=65°

m∠ABC=m∠DEF=65°

m∠ACB=m∠DFE=50°

The three internal angles of the triangles are congruent

therefore

The triangles are similar by AA Similarity Postulate

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noname [10]

Answer:

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Step-by-step explanation:

well when you look at the shape you can go from a to b and count the blocks which it would be 2

and you would want to do the same thing with C,D

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3 years ago

The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and

wariber [46]

Answer:

E 0.923

Step-by-step explanation:

The Z score is a measurement used in statistics to determine the relationship between a value and a mean of a group of values measured as standard deviation from the mean. The z score (z) is given as:

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Given that:

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$z=\frac{x-\mu}{\sigma}=\frac{90-80}{7} =1.43$

From the normal distribution table, P(X < 90) = P(z < 1.43) = 0.923

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3 years ago

if Angela's house is assessed valuation of $61,200 and the tax rate per 100 is $3.78 what will she pay in annual real estate tax

poizon [28]

Answer:

$\boxed{\text{\$2313.40}}$

Step-by-step explanation:

The tax rate is $3.78/$100 assessed

$\text{Tax} = \text{\$61 200 assessed} \times \dfrac{\text{\$3.78}}{\text{\$100 assessed}}$

Cancel the $100 assessed.

612 × $3.78 = $2313.40

Angela's real estate tax will be $\boxed{ \textbf{\$2313.40}}$

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3 years ago

Clark borrow $16,000 to buy a car. He pays simple interest at an annual rate of 6% over a period of 3.5 years. How much does he

Paha777 [63]

The equation for annual interest is A = P(1 + r)^t. We can plug in the known information and get A = 16,000(1 + (0.06))^3.5. Next, we can simplify this equation to A = 16,000(1.06)^3.5. Finally, we raise 1.06 to the power of 3.5 and multiply that by 16,000 and get an answer of $19,619.62.

Hope this helps!

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3 years ago

Read 2 more answers

Mr. Andrews is saving to buy a violin that costs $1,000. He has already saved $450 and decides to put all of this money into a n

Korolek [52]

Answer:

1000=450 (1+ 0.06) y

Step-by-step explanation:

In the paranthesis where it says 0.06 and then 4 at the bottom its supposed to be a fraction btw

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3 years ago