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viva [34]
3 years ago
15

Read the proof. Given: AB ∥ DE Prove: △ACB ~ △DCE We are given AB ∥ DE. Because the lines are parallel and segment CB crosses bo

th lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA. We can state ∠C ≅ ∠C using the reflexive property. Therefore, △ACB ~ △DCE by the AA similarity theorem. SSS similarity theorem. AAS similarity theorem. ASA similarity theorem.

Mathematics
2 answers:
White raven [17]3 years ago
8 0
Pls. see attachment. 

pogonyaev3 years ago
7 0

Answer:

(A) AA similarity

Step-by-step explanation:

Given: AB is parallel to DE.

To prove: △ACB is similar to △DCE.

Proof: It is given that AB is parallel to DE, thus because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines.

Now, from △ACB and △DCE, we have

∠CED≅∠CBA (corresponding angles of transversal CB and are therefore congruent)

and ∠C ≅ ∠C (Reflexive property)

Thus, by AA similarity postulate,

△ACB is similar to △DCE

Hence proved.

Thus, option A is correct.

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In ΔVWX, the measure of ∠X=90°, WX = 8.3 feet, and XV = 2.5 feet. Find the measure of ∠W to the nearest tenth of a degree.
kiruha [24]

Answer:

16.76°

Step-by-step explanation:

In ΔVWX, the measure of ∠X=90°, WX = 8.3 feet, and XV = 2.5 feet.

We want to find the measure of <W.

We know side length that is adjacent and opposite to <W.

We can use the tangent ratio, to find the measure of <W.

The tangent ratio is opposite over hypotenuse.

\tan(m \angle \: w)  =  \frac{2.5}{8.3}

\tan(m \angle \: w)  =  0.301

Take tangent inverse to get:

m \angle \: w= { \tan}^{ - 1}   (0.301)

m \angle \: w=16.76  \degree

7 0
3 years ago
Camilla baked 15 cookies with 3 scoops of flour. How many scoops of flour does Camilla need in order to bake 20 cookies? Solve u
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Answer:

camilla needs 4 scoops of flow because 3 is related to 15 bc "5x3=15" and that gives us to only need 1 more cup to get 20 cookies

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2 years ago
What caused the faulting and uplift in the central Texas ecoregions? a Earthquakes broke the continental crust. b A lot of sedim
devlian [24]

Answer:

Hello! Your answer is, A)Earthquakes broke the continental crust.

Step-by-step explanation:

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3 0
3 years ago
Write the first four terms of the sequence:<br> a = 2<br> an = a(n-1) + 4
eduard

We have sequence equation a_n=a(n-1)+4.

In this case n is a natural number (1, 2, 3, ...).

So start inserting and computing value of a_n given that you know the value of n and a.

a_1=2(1-1)+4=4 (first term)

a_2=2(2-1)+4=6 \\a_3=2(3-1)+4=8 \\a_4=2(4-1)+4=10

Hope this helps.

3 0
3 years ago
Mario took clothes to the cleaners three times last month. first, he brought 3 shorts and 1pair of slacks and $10.96. then, he b
valina [46]

Let us say that:

x = cost of shorts

y = cost of slacks

z = cost of sports coat

 

From the given statements, we can create the following equations:

eqtn 1: 3 x + y = 10.96

eqtn 2:  7 x + 2 y + z = 30.40

eqtn 3:  4 x + z = 14.45

 

Rewrite eqtn 1 explicit to y:

y = 10.96 – 3 x                    --> eqtn 4

 

Rewrite eqtn 3 explicit to z:

z = 14.45 – 4x                     --> eqtn 5

 

Plug in the values of y (eqtn 4) and z (eqtn 5) to eqtn 2:

7 x + 2 (10.96 – 3 x) + 14.45 – 4 x = 30.40

7 x + 21.92 – 6 x + 14.45 – 4 x = 30.40

- 3 x + 36.37 = 30.40

- 3 x = - 5.97

x = 1.99

 

Eqtn 4:

y = 10.96 – 3 x   

y = 10.96 – 3 (1.99)

y = 4.99

 

Eqtn 5:

z = 14.45 – 4x

z = 14.45 – 4 (1.99)

z = 6.49

 

 

Therefore each shirt cost $1.99, each slacks cost $4.99, and each sports coat cost $6.49.

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7 0
3 years ago
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