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3 years ago

Which postulate or theorem proves that these two triangles are congruent?

Mathematics

2 answers:

mario62 [17]3 years ago

5 0

Answer:

ASA postulate of congruency

Step-by-step explanation:

Here Given AE=ED and ∠BAE=∠CDE

Also if we clearly observe ∠AEB=∠CED

By ASA postulate those two triangles are congruent.

The ASA (Angle,Side,Angle) postulate states that if two triangles with two angles and the included angle are equal then the two triangles are congruent.

katrin2010 [14]3 years ago

5 0

Answer:

<h2>ASA postulate of congruence.</h2>

Step-by-step explanation:

The ASA postulate refers to the congruence of Angle-Side-Angle pairs. In this problem we have ABE and DCE triangle. The reasons why we can use ASA postulate are:

We can see that angles DEC and AEB are congruent, because they are opposite angles.
Side AE is congruent with side DE, it's part of the hypothesis of the problem.
Also, angle A is congruent with angle D, by hypothesis.

So, there are three pairs of congruence, Angle-Side-Angle. Therefore, according to ASA postulate, we can say that the triangle ABE is congruent with triangle DCE.

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polet [3.4K]

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6 0

3 years ago

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Tatiana [17]

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4 0

3 years ago

Read 2 more answers

genetic experiment with peas resulted in one sample of offspring that consisted of green peas and yellow peas. a. Construct a %

Andreas93 [3]

Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The 95% confidence interval is $0.2392 < p < 0.3108$

No, the confidence interval includes 0.25, so the true percentage could easily equal 25%

Step-by-step explanation:

From the question we are told that

The total sample size is $n = 432 + 164 =596$

The number of offspring that is yellow peas is $y = 432$

The number of offspring that is green peas is $g = 164$

The sample proportion for offspring that are yellow peas is mathematically evaluated as

$\r p = \frac{ 164 }{596}$

$\r p = 0.275$

Given the the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = (100 - 95)\%$

$\alpha = 5\% = 0.0 5$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }$

=> $E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }$

=> $E = 0.0358$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

=> $0.275 - 0.0358 < p < 0.275 + 0.0358$

=> $0.2392 < p < 0.3108$

6 0

3 years ago

Taxes on 100 dlls??

dezoksy [38]

The sales tax is 6.25% from $100

8 0

3 years ago

What is the coefficient of the second term of the trinomial?

marin [14]

The coefficient of the second term is 18.

What you do is you FOIL the terms:
$(3x+3)(3x+3)\\ Multiply\ the\ first\ terms\ together:\\ 3x*3x=9x^{2}\\ Then\ the\ outer\ terms:\\ 3x*3=9x\\ Next,\ the\ inner\ terms:\\ 3x*3=9x\\ Finally,\ multiply\ the\ last\ terms:\\ 3*3=9\\ Putting\ the\ terms\ together:\\ 9x^{2}+9x+9x+9=9x^{2}+18x+9\\\\ Since\ (3x+3)^{2}=9x^{2}+Bx+9=9x^{2}+18x+9,\ then \ B=18.$

7 0

3 years ago

Read 2 more answers