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3 years ago

What else would need to be congruent to show that ABC XYZ by ASA?

Mathematics

2 answers:

Naddik [55]3 years ago

8 0

Answer: The correct option is (D) AC ≅ XZ.

Step-by-step explanation: Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

Thus, (D) is the correct option.

docker41 [41]3 years ago

5 0

Side XZ needs to be congruent to side AC. The answer is D.

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How do you solve this?

slavikrds [6]

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3 years ago

Assume you know that a hot-air balloon is currently inflated with a certain amount of air and that the amount is a percent of th

Gemiola [76]

Answer:

Percent air is calculated as:

Percent air = Current amount/Total amount *100

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3 years ago

Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of

Anastaziya [24]

Answer:

325

Step-by-step explanation:

You must have heard about Arithmetic Progressions (AP)

Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

Our very own counting numbers form AP

For example :-

2 = 1 + 1

3 = 2 + 1

4 = 3 + 1

The number in bold (1) is that constant number which is added to a number to form its successive number.

To find the sum of series forming AP, we use the formula :-

$sum = \frac{n}{2} \{ a + a _{n} \}$

here,

n is the number of terms
a is the first number of the series
an is the last number of the series

So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

and n is 25

$S = \frac{25}{2}\{ 1 +25\}$

$= \frac{25 \times 26}{2}$

$= 25 \times 13$

$= 325$

So, the value of S comes out to be 325.

8 0

3 years ago

Read 2 more answers

Find the exact values of sin2 θ for cos θ = 3/18 on the interval 0° ≤ θ ≤ 90°

mote1985 [20]

Answer:

$sin(2\theta)=\frac{\sqrt{35} }{18}$

Step-by-step explanation:

Recall the formula for the sine of the double angle:

$sin(2\theta)=2*sin(\theta)*cos(\theta)$

we know that $cos(\theta)=\frac{3}{18}$ , and that $\theta$ is in the interval between 0 and 90 degrees, where both the functions sine and cosine are non-negative numbers. Based on such, we can find using the Pythagorean trigonometric property that relates sine and cosine of the same angle, what $sin(\theta)$ is:

$cos^2(\theta)+sin^2(\theta)=1\\sin^2(\theta)=1-cos^2(\theta)\\sin(\theta)=\sqrt{1-cos^2(\theta)} \\sin(\theta)=\sqrt{1-(\frac{3}{18} )^2}\\sin(\theta)=\sqrt{1-\frac{9}{324} }\\sin(\theta)=\sqrt{\frac{324-9}{324} }\\sin(\theta)=\sqrt{\frac{315}{324} }\\\\sin(\theta)=\frac{3}{18}\sqrt{35 }$

With this information, we can now complete the value of the sine of the double angle requested:

$sin(2\theta)=2*sin(\theta)*cos(\theta)\\sin(2\theta)=2*\frac{3}{18} \,\sqrt{35} \,\frac{3}{18}\\sin(2\theta)=\frac{2*3*3}{18*18}\,\sqrt{35} \\sin(2\theta)=\frac{\sqrt{35} }{18}$

6 0

3 years ago

The temperature changes can be represented by the expression -0.5( 1 -2h).Chase says that the temperature change can also be rep

UNO [17]

Answer:

The expression are equivalent

Step-by-step explanation:

The question requests that we show whether the equation -0.5( 1 -2h) is equivalent to 4(2h + 2) - 7h - 8.5 or not :

Simplifying 4(2h + 2) - 7h - 8.5 ; we have ;

4(2h + 2) - 7h - 8.5

8h + 8 - 7h - 8.5

8h - 7h + 8 - 8.5

h - 0.5

-0.5(1 - 2h)

-0.5 + h

= h - 0.5

Hence, both expressions are the same

3 0

3 years ago