Tutors Answer Your Questions about Geometry proofs (FREE)
Question 1210478: Let XYZ be a triangle, and let XP, XQ, XR be the altitude, angle bisector, and median from X, respectively. If angle YQZ = 90^\circ and angle ZQX = 22^\circ, then what is the measure of angle RZP in degrees?
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Question 1210478: Let XYZ be a triangle, and let XP, XQ, XR be the altitude, angle bisector, and median from X, respectively. If angle YQZ = 90^\circ and angle ZQX = 22^\circ, then what is the measure of angle RZP in degrees?
Click here to see answer by ikleyn(53213)  |
Question 1166185: The grid below contains one large square divided into four small squares. There is one circle on each corner of the smaller squares, so 9 in total
(I can't provide a photo of the figure so hopefully my description is understandable).
Q)Show that, up to rotation and reflection, there is only one way to fill the
empty circles with the numbers 1 to 9 so that the sums of the numbers at
the vertices of all five squares are the same.
Thanks!
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Question 1210493: Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. If the area of triangle $PQR$ is $12$, then what is the area of triangle $XYZ$?
Click here to see answer by CPhill(2103) |
Question 1210493: Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. If the area of triangle $PQR$ is $12$, then what is the area of triangle $XYZ$?
Click here to see answer by ikleyn(53213) |
Question 1210492: In triangle ABC, M is the midpoint of \overline{BC}, E is the midpoint of \overline{AB}, and D is the midpoint of \overline{AM}. Point T is the intersection of \overline{BD} and \overline{ME}. Find the area of triangle XYZ if [ABC] = 14.
Click here to see answer by CPhill(2103) |
Question 1210492: In triangle ABC, M is the midpoint of \overline{BC}, E is the midpoint of \overline{AB}, and D is the midpoint of \overline{AM}. Point T is the intersection of \overline{BD} and \overline{ME}. Find the area of triangle XYZ if [ABC] = 14.
Click here to see answer by ikleyn(53213) |
Question 731826: Provide the reasons for the proof.
Given: m angle 1 = m angle 2
Prove: (line over)AC(up-side down T)(line over)BD
Statements:
a. m angle 1 = m angle 2
b. Angle 1 is supplementary to angle 2
c. m angle 1 + m angle 2= 180 degrees
d. m angle 1 + m angle 2 +180 degrees
2(m angle 1)= 180 degrees
e. m angle 1 = 90 degrees
f. angle 1 is a right angle
g.(line over)AC(up-side down T)(line over)BD
Reasons:
a. given
b. ?
c. ?
d. ?
e. ?
f. ?
g. ?
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Question 1210500: In trapezoid PQRS, Base PQ is parallel to base RS. Let point X be the intersection of diagonals PR and QS. The area of triangle PQR is 4 and the area of triangle QRX is 4. Find the area of trapezoid PQRS
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Question 1210498: Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EBC$ is $4,$ and the area of triangle $ABC$ is $4.$ Find the area of parallelogram $ABCD$.
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Question 1210498: Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EBC$ is $4,$ and the area of triangle $ABC$ is $4.$ Find the area of parallelogram $ABCD$.
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Question 1210497: In trapezoid $EFGH,$ $\overline{EF} \parallel \overline{GH},$ and $P$ is the point on $\overline{EH}$ such that $EP:PH = 1:1$. If the area of triangle $PEG$ is $4$, and the area of triangle $EFG$ is $4$, then find the area of trapezoid $EFGH$.
Click here to see answer by CPhill(2103) |
Question 1210497: In trapezoid $EFGH,$ $\overline{EF} \parallel \overline{GH},$ and $P$ is the point on $\overline{EH}$ such that $EP:PH = 1:1$. If the area of triangle $PEG$ is $4$, and the area of triangle $EFG$ is $4$, then find the area of trapezoid $EFGH$.
Click here to see answer by ikleyn(53213) |
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