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IgorLugansk [536]
3 years ago
6

Determine whether the two triangles can be proven congruent using the AAS congruence method. If they can, select the congruence

statement. answers: A) ΔABC ≅ ΔEDC B) ΔCBA ≅ ΔCED C) The triangles aren't congruent using AAS. D) ΔCAB ≅ ΔEDC

Mathematics
2 answers:
Ierofanga [76]3 years ago
5 0

Answer:

A) triangle ABC is congruent to triangle EDC

Step-by-step explanation:

The AAS method of proving congruence of triangles uses two angles and a non-included side of the triangle. If two angles and the non-included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Let's see what we have in this problem:

<ACB and <ECD are congruent since they are vertical angles.

<A and <E are congruent by given.

Sides AB and ED are non-included sides and are congruent.

Since we have two angles and a non-included side of a triangle and the corresponding parts of another triangle, the triangles are congruent by AAS.

Now we need the statement of congruence.

Angles ACB and ECD are corresponding angles, so the letter C must appear in both triangles in the same position.

Angles A and E are corresponding angles, so the letters A and E must appear in both triangles the same position.

We already have CA and CE. The last angles left are corresponding angles B and D, so we get triangle CAB and triangle CED. Since a triangle may be named using any order of the vertices, we can rename the triangles ABC and EDC and maintain the same corresponding vertices.

Answer: A) triangle ABC is congruent to triangle EDC

Dmitry_Shevchenko [17]3 years ago
3 0

Answer:

The A) ΔABC ≅ ΔEDC

Step-by-step explanation:

The AAS congruence method requires 2 angles and their un-included side to be congruent. ∠A ≅ ∠E due to the markings, ∠C ≅ ∠C because they are vertical angles, and AB ≅ ED due to the markings. 2 angles and their un-included side are congruent.

As for the congruence statement, A is the correct answer because ∠A ≅ ∠E, ∠B ≅ ∠D, and ∠C ≅ ∠C. The order of the naming of the triangles aligns to the angle's congruence.

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The stadium has 53,000 seats seats sell for $42 in section 8 $36 in section B $30 in section C the number of seats in this in se
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Answer:

Section A = 26,500 seats

Section B = 14,900 seats

Section C = 11,600 seats

Step-by-step explanation:

Total seats = 53,000

Total revenue = 1,997,400

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Section B seat = $36

Section C seat = $30

The number of seats in this in section A equals the total number of seats in section BNC

A = B + C

A + B + C = 53,000 (1)

42A + 36B + 30C = 1,997,400 (2)

Substitute A = B + C into (1)

A + B + C = 53,000

B + C + B + C = 53,000

2B + 2C = 53,000

2(B + C ) = 53,000

B + C = 53,000 / 2

= 26,500

B + C = 26,500 (3)

Substitute B + C = 26,500 into (2)

42A + 36B + 30C = 1,997,400

Recall,

A = B + C

42( 26,500) + 36B + 30C = 1,997,400

1,113,000 + 36B + 30C = 1,997,400

36B + 30C = 1,997,400 - 1,113,000

36B + 30C = 884,400. (4)

Multiply (3) by 30

B + C = 26,500 × 30

30B + 30C = 795,000 (5)

36B + 30C = 884,400 (4)

Subtract (5) from (4) to eliminate C

36B - 30B = 884,400 - 795,000

6B = 89,400

B = 89,400/6

= 14,900

B = 14,900

From (3)

B + C = 26,500

C = 26,500 - B

= 26,500 - 14,900

= 11,600

A = B + C

= 14,900 + 11,600

= 26,500

Section A = 26,500 seats

Section B = 14,900 seats

Section C = 11,600 seats

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Currently, we have $120, the amount earned, and 2 days, the current rate.
Our fraction for this is: 120 / 2 = x / 6, x being the amount earned in 6 days.

Let's use a little technique to help us answer faster.

With our current money earned, 120, and our current days, 2, we can divide 120 by 2 to find out how many we earned in 1 day.

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With this formula, 60d, d being the amount of days, we can solve quicker.

We are solving for 6 days, so multiply $60 by 6 days.

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