What does the ratio 1/5 to 1/2 equal to simplified
1 answer:
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Answer:
= 20 - 9n
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 2 - 11 = - 7 - 2 = - 9
This indicates the sequence is arithmetic with nth term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 11 and d = - 9 , then
= 11 - 9(n - 1) = 11 - 9n + 9 = 20 - 9n
Refer to the attached diagram for further a visual explanation. As per the given information, segments (AB) and (AD) are congruent. Moreover, segments (AC) and (AE) are also congreunt. One is also given that angles (<BAD) and (<EAC) are congruent. However, in order to prove the triangles (ABC) and (ADE) are congruent (using side-angle-side) congruence theorem, one needs to show that angles (<BAC) and (<DAE) are congruent. An easy way to do so is to write out angles (<BAC) and (<DAE) as the sum of two smaller angles:
<BAC = <BAD + <DAC
<DAE = <DAC + <EAC
Both angles share angle (DAC) in common, since angles (<EAC) and (BAD) are congruent, angles (<BAC) and (<DAE) must also be congruent.
Therefore triangles (ABC) and (ADE) are congruent by side-angle-side, thus sides (BC) and (DE) must also be congruent.
In summary:
AB = AD Given
AC = AE Given
<BAD = <EAC Given
<DAC = <DAC Reflexive
<BAC = <BAD + <DAC Parts-Whole Postulate
<DAE = <EAC + < DAC Parts-Whole Postulate
<BAC = <DAE Transitivity
ABC = ADE Side-Angle-Side
BC = DE Corresponding parts of congruent triangles are congruent
