Tutors Answer Your Questions about Geometry proofs (FREE)
Question 1210512: Shown below is rectangle $EFGH$. Its diagonals meet at $Y$. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If $FY = 24$ and $HX = 28$ and $EF = 10$, find the perimeter of rectangle $EFGH$.
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Question 1210506: What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What kind of quadrilateral has the property that all four angles are right angles? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length and all four angles are right angles? Select all that apply.
What kind of quadrilateral has the property that exactly one pair of opposite sides is parallel? Select all that apply.
What kind of quadrilateral has the property that its diagonals bisect each other? Select all that apply.
What kind of quadrilateral has the property that its diagonals are congruent (equal in length)? Select all that apply.
What kind of quadrilateral has the property that its diagonals are perpendicular bisectors of each other? Select all that apply.
What kind of quadrilateral has the property that its diagonals are perpendicular? Select all that apply.
What kind of quadrilateral has the property that all vertices lie on a single circle (cyclic quadrilateral)? Select all that apply.
What kind of quadrilateral has the property that it is a trapezoid, and the two non-parallel sides (legs) are equal in length? Select all that apply.
What kind of quadrilateral has the property that the sum of the measures of its consecutive angles is $180^\circ$? Select all that apply.
What kind of quadrilateral has the property that the diagonals of the quadrilateral always divide it into four congruent triangles of equal area? Select all that apply.
What kind of quadrilateral has the property that two pairs of adjacent sides are equal in length, but all four sides are not equal? Select all that apply.
What kind of quadrilateral has the property that the lengths of its diagonals are equal, and the diagonals are perpendicular? Select all that apply.
What kind of quadrilateral has the property that the distance between the two parallel sides is constant? (This is a more descriptive property for a specific type). Select all that apply.
What kind of quadrilateral has the property that its diagonals bisect the interior angles? Select all that apply.
What kind of quadrilateral has the property that it is a rectangle, but it is not a square? Select all that apply.
What kind of quadrilateral has the property that its diagonals are congruent and bisect each other, but they are not perpendicular? Select all that apply.
What kind of quadrilateral has the property that its opposite angles are congruent? Select all that apply.
What kind of quadrilateral has the property that the segments connecting the midpoints of its consecutive sides form a rhombus? Select all that apply.
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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 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 $EFGH$.
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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 $EFGH$.
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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 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 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 $XYZ$?
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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 $XYZ$?
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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.
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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.
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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 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?
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780
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