Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?
2 answers:
Answer:
IV,III,I,II
Step-by-step explanation:
We are given that a triangle ABC in which three medians are given .
We are given a proof of three medians of a triangle which intersect at common point.
We have to find which is the most logical order of statement and justifications I,II,III and IV to complete the proof.
Statement:Point F is the mid- point of segment AB and point E is the mid-point of segment AC.
Draw segment BE and draw segment FC.
Justification: By construction
Statement: Point G is the point of intersection of segment BC and segment FC.
Justification: Intersecting lines postulate
Statement:Draw segment AG.
Justification: By construction
Statement:Point D is the mid- point of intersection between segment AG and segment BC.
Justification: Intersecting lines postulate
Statement:Point H lies on segment AG such that
Justification: By construction
Step:IV
Justification: Midpoint segment theorem
Step III.
Justification: Substitution
Step I.BGCH is parallelogram
Justification: By property of parallelogram (Opposite sides are parallel)
StepII:
Justification: Property of parallelogram (diagonals of parallelogram bisect each other)
Statement: AD is median
Justification: Definition of median
Answer:IV,III,I,II
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(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj
Specifically,
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feet.
Please be sure your calculator is set to degrees (not radians) when you do this problem.
(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.
sin = opp/hyp. As the sin Q = 9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.
cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.
You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.
Specifically,
Please be sure your calculator is set to degrees (not radians) when you do this problem.
(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.
sin = opp/hyp. As the sin Q = 9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.
cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.
You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.