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postnew [5]
3 years ago
5

In triangle ABC shown below, DE is parallel to AC. The following two-column proof with missing statements and reasons proves tha

t if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally: Which statement and reason accurately completes the proof? A. 3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate 4. ∠A ≅ ∠C; Isosceles Triangle Theorem B. 3. ∠BDE ≅ ∠BAC; Alternate Interior Angles Theorem 4. ∠A ≅ ∠C; Isosceles Triangle Theorem C. 3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate 4. ∠B ≅ ∠B; Reflexive Property of Equality D. 3. ∠BDE ≅ ∠BAC; Alternate Interior Angles Theorem 4. ∠B ≅ ∠B; Reflexive Property of Equality

Mathematics
1 answer:
lianna [129]3 years ago
5 0

Answer:

The correct option is;

C. 3. ∠BDE ≅∠BAC, Corresponding Angles Postulate 4. ∠B ≅ ∠B Reflexive Property of Equality

Step-by-step explanation:

The two column proof can be written as follows;

Statement,                         Reason

1. \overline{DE} \parallel \overline{AC},                           Given

2. \overline {AB} is a transversal ,         Conclusion from statement 1.

We note that ∠BDE  and ∠BAC are on the same side of the transversal relative to the parallel lines, and are therefore, corresponding angles.

Therefore, we have;

3. ∠BDE ≅∠BAC,                 Corresponding Angles Postulate

Also

4. ∠B ≅ ∠B,                           Reflexive Property of Equality

In the two triangles, ΔABC and ΔDBE, we have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

From ∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B +  ∠BCA = 180°

Therefore, ∠BED = ∠BCA Substitution property of equality

Which gives;

5, ΔABC ~ ΔDBE,          Angle Angle Similarity Postulate

6. BD/BA = BE/BC,      Converse of the Side-Side-Side Similarity Theorem

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3 years ago
Write a recrusive rule for the exponential function<br>f(x)=0.25(2/3)^x​
krok68 [10]

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f(0) = 0.25 = 1/4

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Step-by-step explanation:

a0 = 0.25×(2/3)⁰ = 0.25×1 = 0.25 = 1/4

a1 = 0.25×(2/3)¹ = 0.25×(2/3) = 1/4 × 2/3 = 2/12 = 1/6 =

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a2 = 0.25×(2/3)² = 0.25×(4/9) = 1/4 × 4/9 = 4/36 = 1/9 =

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2 years ago
In the figure below, BCA ~ STR. Find cos C, sin C, and tan C. Round your answers to the nearest hundredth.
arsen [322]

Answer:

\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63

Step-by-step explanation:

According to the trigonometric ratios in aright triangle :

\sin x =\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}\\\\\cos x =\dfrac{\text{Side adjacent to x}}{\text{Hypotenuse}}\\\\\tan x=\dfrac{\sin x}{\cos x}

Given:  ΔBCA ~ ΔSTR

Since , corresponding angles of two similar triangles are equal.

So, ∠C = ∠T                            ...(i)    [Middle letter]

In triangle STR

\sin T=\dfrac{\text{Side opposite to T}}{\text{Hypotenuse}}\\\\=\dfrac{26.4}{30.9}\approx0.85\\\\\cos x =\dfrac{\text{Side adjacent to T}}{\text{Hypotenuse}}\\\\=\dfrac{16.2}{30.9}\approx0.52\\\\\tan T=\dfrac{\sin T}{\cos T}\\\\=\dfrac{0.85}{0.52}\approx1.63  ...(ii)

From (i) and (ii), we have

\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63

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For the year previous to that one, he had:

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