Please help me write a 2 column proof AB parallel to DC ; BC parallel to AE prove BC/EA = BD/EB
1 answer:
Answer and Step-by-step explanation:
Since it is given that
AB || DC
BC || AE
Based on this we can conclude that
If AB || DC
So we can say
∠ABE ≅ ∠CDB
This indicates that the alternate interior angles are congruent i.e its angle and sides are equal
Now
If BC || AE
So we can say
∠CBD ≅ ∠BEA
This indicates that the alternate interior angles are congruent i.e its angle and sides are equal
Now
ΔAEB is same as ΔCBD
This indicates that in one triangle two angles are same to another two angles so both triangles are similar to each other i.e this is a AA Similarity Postulate
Finally we proof
As the same sides are proportional to each other
We compared both based on interior angles
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Answer:
Of the given geometric sequence, the first term a is 6 and its common ratio r is 2.
Step-by-step explanation:
Recall that the direct formula of a geometric sequence is given by:
Where <em>T</em>ₙ<em> </em>is the <em>n</em>th term, <em>a</em> is the initial term, and <em>r</em> is the common ratio.
We are given that the fifth term <em>T</em>₅ = 96 and the eighth term <em>T</em>₈ = 768. In other words:
Substitute and simplify:
We can rewrite the second equation as:
Substitute:
Hence:
So, the common ratio <em>r</em> is two.
Using the first equation, we can solve for the initial term:
In conclusion, of the given geometric sequence, the first term <em>a</em> is 6 and its common ratio <em>r</em> is 2.