Geometric Relations: need worked solutions to geom. Q's

[Eucliann]

So our Geometry teacher gave us some assignments that are related to our lessons but not necessarily directly discussed.
You can find the problems here: https://picasaweb.google.com/1125972462 ... 4936053634
I don't need ALL the answers because I already have most of them, though answers with solutions are very much appreciated so that I can double-check my work.
Basically, I'm not sure on Problems 2, 3 and 4 in Collineary and Betweeness; 3 and 4 in Congruent Angles; and number 3 in Angle Pairs.

Thanks so much!! <3
~Ann

[stapel_eliz]

Note to poster: As you read in the "Read Before Posting" message, volunteers do not "do" students' work for them, nor do they give out answers. Students need to show at least some effort toward the solutions.

Also, please clarify the first "Question 3" below. In particular, are you needing to find the probability that the random point is six units "from" Q, or the probability that the point is "within" six units "of" Q? (As currently posted, the English doesn't make sense.)

You can find the problems here: https://picasaweb.google.com/1125972462 ... 4936053634
... I'm not sure on Problems 2, 3 and 4 in Collineary and Betweeness; 3 and 4 in Congruent Angles; and number 3 in Angle Pairs.

Note to volunteers: The exercises in question are as follows:

Collinearity:

2) Points A, B, C, and D are on a straight line in that order, and there is a point P not on this line such that PD = (5/2)PD and AB = CD. If the area of triangle PAB is 100 square units, find the area of triangle PCD.

3) Draw a diagram in which F is between A and E, F is also between R and S, but A, E, R, and S are non-collinear.

4) The coordinate of P, Q, and R are -6, 20, and 24, respectively. If a point is chosen at random on segment PR, what is the probability that it is six units of Q?

Congruent Angles:

3) Two lines bisect consecutive angles of a regular heptagon and intersect in the heptagon's interior. Find the measures of the angles formed by the intersecting lines.

4) Ray BE bisects angle A of DABC and ray CE bisects angle C of DABC. If the measure of angle A is 84 degrees, find the measure of the angle formed by the intersecting rays BE and CE.

Angle Pairs:

3) The ratio of the complements of two angles is 3 : 2, and the ratio of their supplements is 9 : 8. Find the [measures of] the two original angles.

[Eucliann]

Note to poster: As you read in the "Read Before Posting" message, volunteers do not "do" students' work for them, nor do they give out answers. Students need to show at least some effort toward the solutions.

D'oh!! I'd been SURE I put those in before I hit submit...what happened? O_O Ah well. I'll just re-type them again I guess.

Also, please clarify the first "Question 3" below. In particular, are you needing to find the probability that the random point is six units "from" Q, or the probability that the point is "within" six units "of" Q? (As currently posted, the English doesn't make sense.)

That is exactly the reason why I can't solve it. That is what the questions say, word-by-word, on the problem sheet. No clarifications at all :(

2) Points A, B, C, and D are on a straight line in that order, and there is a point P not on this line such that PD = (5/2)PB and AB = CD. If the area of triangle PAB is 100 square units, find the area of triangle PCD.

I get that the area of a triangle is (bh)/2, so if AB=x, 200/x=height. Since AB=CD, CD=x too. That's all that I can work out from the given @_@
I don't get how PD=(5/2)PB is related. is PD Triangle PDC's height? If so, then is PB triangle PBA's height?

3) Draw a diagram in which F is between A and E, F is also between R and S, but A, E, R, and S are non-collinear.

I don't see how it's possible to diagram these if they're all non-collinear. If there are more than three points, then are they all non-collinear if only one point lies outside the line the others are on? Or does that mean that none of them must ever be in the same line?

4) The coordinate of P, Q, and R are -6, 20, and 24, respectively. If a point is chosen at random on segment PR, what is the probability that it is six units of Q?

Like I said, I don't know how to approach this because it isn't clarified if it means "six units from Q" or "within six units of Q".

Congruent Angles:

3) Two lines bisect consecutive angles of a regular heptagon and intersect in the heptagon's interior. Find the measures of the angles formed by the intersecting lines.

What does 'consecutive angles' mean? Two angles beside/adjacent to each other? If it's a regular heptagon, then they must be equal. So the bisectors should probably be equal too, right? But what is the measure of one angle in a right heptagon? I don't know. :(

4) Ray BE bisects angle A of DABC and ray CE bisects angle C of DABC. If the measure of angle A is 84 degrees, find the measure of the angle formed by the intersecting rays BE and CE.

What kind of figure is DABC anyways? I'm fairly sure I could answer this, but I can't visualize the problem properly.

Angle Pairs:

3) The ratio of the complements of two angles is 3 : 2, and the ratio of their supplements is 9 : 8. Find the [measures of] the two original angles.

No need to answer. I solved it already

[buddy]

2) Points A, B, C, and D are on a straight line in that order, and there is a point P not on this line such that PD = (5/2)PB and AB = CD. If the area of triangle PAB is 100 square units, find the area of triangle PCD.

I get that the area of a triangle is (bh)/2, so if AB=x, 200/x=height. Since AB=CD, CD=x too. That's all that I can work out from the given @_@
I don't get how PD=(5/2)PB is related. is PD Triangle PDC's height? If so, then is PB triangle PBA's height?

I get the same thing. The formula is A = (1/2)bh, and b and h are the same, so A has to be the same. I don't get the point of the (5/2)PB???

3) Draw a diagram in which F is between A and E, F is also between R and S, but A, E, R, and S are non-collinear.

I don't see how it's possible to diagram these if they're all non-collinear. If there are more than three points, then are they all non-collinear if only one point lies outside the line the others are on? Or does that mean that none of them must ever be in the same line?

If they mean that not all four points are collinear together (maybe two or three at a time are, but not all four), then do two segments that cross at F.

4) The coordinate of P, Q, and R are -6, 20, and 24, respectively. If a point is chosen at random on segment PR, what is the probability that it is six units of Q?

I don't know how to approach this because it isn't clarified if it means "six units from Q" or "within six units of Q".

Yeh, without that you can't answer this. I'm pretty sure the answer changes if the question changes, and "equal to" is different that "within".

Congruent Angles:

3) Two lines bisect consecutive angles of a regular heptagon and intersect in the heptagon's interior. Find the measures of the angles formed by the intersecting lines.

What does 'consecutive angles' mean? Two angles beside/adjacent to each other? If it's a regular heptagon, then they must be equal. So the bisectors should probably be equal too, right? But what is the measure of one angle in a right heptagon? I don't know. :(

Didn't they tell you the definitions and formulas in class??? You can find them online: consecutive angles, angle measure in regular polygons.

4) Ray BE bisects angle A of DABC and ray CE bisects angle C of DABC. If the measure of angle A is 84 degrees, find the measure of the angle formed by the intersecting rays BE and CE.

What kind of figure is DABC anyways? I'm fairly sure I could answer this, but I can't visualize the problem properly.

They don't say, so it's just some kind of quadrilateral. Draw something like a squished rectangle, and run with it.