Given that lines AB and DE are parallel,determine how triangles ABC and EDC can be shown to be similar

Mathematics

2 answers:

Kobotan [32]3 years ago

5 0

Answer:

Step-by-step explanation:

Draw the two triangles so the two triangles share point C. It should look like a bowtie.

(1) AB is parallel to DE Given

(2) Angle A = Angle D If two parallel lines are cut by a transversal, alternate interior angles are equal.

Angle B = Angle E

(3) Angle BCA = Angle DCE Vertical angles are equal.

(4) Triangle BAC is similar to Triangle DEC If 3 angles in one triangle are equal to three angles in another triangle, the triangles are similar.

(5) AB/DE = AC/EC If two triangles are similar, corresponding sides are proportional.

Roman55 [17]3 years ago

3 0

Answer:

The transversals cutting through the parallel lines create angles that are congruent to one another. Angles 1`and 5 are alternate interior and are congruent. Angles 2 and 6 are alternate interior and are congruent. And of course if 2 of 3 angles in 2 triangles are congruent, then the 3rd angles have to be congruent as well. HOWEVER, we can see that the sides are NOT congruent, and we need at least one side to prove congruency. Since we have 3 congruent angles, we can only say they are similar.

Step-by-step explanation:

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1. the sum of the first n odd positive integers is 64. what is the value of n ?

chubhunter [2.5K]

The value of the n is 8.
There are 7 positive integers between 100 and 200 which are divisible by 14.

Step-by-step explanation:

The sum of first n odd positive integer is n^2. The nth odd number is 2n-1.

i.e. 1 + 3 + ........+ (2n-1) = n^2.

1 + 3 +..........+ (2n-1) = 64

n^2 = 64

n = 8.

The positive integers between 100 and 200 which are divisible by 14 are 112, 126, 140, 154, 168, 182, 196. It is obtained by the multiples of 14 between 100 and 200.

100 = 7 * 14 + 2

200 = 14 * 14 + 4. The answer is 14 - 7 = 7

The seven numbers are

14 * 8 = 112

14 * 9 = 126

14 * 10 = 140

14 * 11 = 154

14 * 12 = 168

14 * 13 = 182

14 * 14 = 196

6 0

3 years ago