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3 years ago

Which method would you use to prove that the two triangles are congruent?

Mathematics

2 answers:

prisoha [69]3 years ago

4 0

Answer: The correct option is (A) SAS.

Step-by-step explanation: We are given to select the method that would be used to prove that the two triangles are congruent.

Let us name the given triangles as ABC and EBD as shown in the attached figure below.

Then, according to the given information, we have

$AB=BD\\\intertext{and}\\BC=EB.$

Also, ∠ABC and ∠EBD are vertically opposite angles, so they must have equal measures.

That is,

$m\angle ABC=m\angle EBD.$

So, in triangles ABC and EBD, we have

$AB=BD,\\\\BC=EB\\\\\intertext{and}\\m\angle ABC=m\angle BED.$

That is, two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of the other triangle.

Therefore, by side-angle-angle postulate, the two triangles are congruent.

Thus,

ΔABC ≅ ΔEBD (SAS postulate).

Option (A) is CORRECT.

jeka57 [31]3 years ago

3 0

Answer:

SAS

Step-by-step explanation:

Side

Two congruent legs on each triangle

Angle

The vertical angle in between makes both of the angles congruent.

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julsineya [31]

Answer:

i think it's an orca-dontist

Step-by-step explanation:

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3 years ago

Solve for x: (8x + 15) = 24

Hatshy [7]

Answer:

Step-by-step explanation:

8x + 15 = 24

8x = 9

x = $\frac{9}{8}$

7 0

3 years ago

Read 2 more answers

Assume the sample variances to be continuous measurements. Find the probability that a random sample of 25observations, from a n

konstantin123 [22]

Answer:

a) $P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

b) $P(13.848$ Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

For this case we assume that the sample variance is given by $S^2$ and we select a random sample of size n from a normal population with a population variance $\sigma^2$ . And we define the following statistic:

$T = \frac{(n-1) S^2}{\sigma^2}$

And the distribution for this statistic is $T \sim \chi^2_{n-1}$

For this case we know that n =25 and $\sigma^2 = 6$ so then our statistic would be given by:

$\chi^2 = \frac{(n-1)S^2}{\sigma^2}=\frac{24 S^2}{6}= 4S^2$

With 25-1 =24 degrees of freedom.

Solution to the problem

Part a

For this case we want this probability:

$P(S^2 > 9.1)$

And we can multiply the inequality by 4 on both sides and we got:

$P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"

Part b

For this case we want this probability:

$P(3.462 < S^2$

If we multiply the inequality by 4 on all the terms we got:

$P(3.462*4 < 4S^2 < 4*10.745)= P(13.848< \chi^2$ And we can find this probability like this: $P(13.848$ And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

8 0

3 years ago

Solve -8x + 4 ≤ 36 A. x ≥ -4 B. x ≤ 4 C. x ≥ 4 D. x ≤ -4

nexus9112 [7]

- 8x + 4 ≤ 36
Subtract 4 from both sides.
-8x ≤ 32
Divide both sides by -8. When dividing by a negative number change the
x ≥ - 4 inequality sign.
Letter A

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3 years ago

Which value(s) from the set {5,7,9,11,13} make the inequality w-4<8 true?

Allisa [31]

Rewrite the inequality as

$w$

by adding 4 to both sides.

So, you want to pick only the values that are strictly less than 12, i.e. all of the values except 13.

6 0

3 years ago