Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete
d the proof incorrectly? Explain.
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1 answer:
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The turtle population will be 486 after 5 years.
<u>Step-by-step explanation</u>:
The general form of a geometric progression or geometric sequence is a, ar, ar², ar³ and so on.
where,
- a = first term
- r = common ratio
<u>The formula to find the nth term in GP is :</u>
nth term =
The given sequence 6,18,54.
In this sequence,
- The first term, a = 6
- The common ratio, r = 18/6 = 3
5th term =
⇒
⇒ 681
⇒ 486
Therefore, after 5 years the population will be 486.
<u>Question 4</u>
1) bisects
,
, and
(given)
2) (an angle bisector splits an angle into two congruent parts)
3) and
are right angles (perpendicular lines form right angles)
4) and
are right triangles (a triangle with a right angle is a right triangle)
5) (reflexive property)
6) (HA)
<u>Question 5</u>
1) and
are right angles,
,
is the midpoint of
(given)
2) and
are right triangles (a triangle with a right angle is a right triangle)
3) (a midpoint splits a segment into two congruent parts)
4) (HA)
5) (CPCTC)
<u>Question 6</u>
1) and
are right angles,
bisects
(given)
2) (reflexive property)
3) (an angle bisector splits an angle into two congruent parts)
4) and
are right triangles (a triangle with a right angle is a right triangle)
5) (HA)
6) (CPCTC)
7) bisects
(if a segment splits an angle into two congruent parts, it is an angle bisector)
<u>Question 7</u>
1) and
are right angles,
(given)
2) and
are right triangles (definition of a right triangle)
3) (vertical angles are congruent)
4) (transitive property of congruence)
5) (reflexive property)
6) (HA theorem)
7) (CPCTC)
8) bisects
(definition of bisector of an angle)