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2 years ago

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

Mathematics

1 answer:

omeli [17]2 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°

Find the measure of angle ACB

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°

Find the measure of angle DEF

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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2 years ago

a bag contains eleven counters. five are white. a counter is taken out the bag and is not replaced. a second counter is taken ou

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Answer:

$\displaystyle P(A)=\frac{6}{11}$

Step-by-step explanation:

Probabilities

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Let's call W to the event of picking a white counter in any of the two extractions, and N when the counter is not white. The sample space of the random experience is

$\Omega=\{WW,WN,NW,NN\}$

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$\displaystyle \frac{5}{11}$