Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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one angle of an isosceles triangle measures 46°. what measures are poss…
A. $67^{\circ}$, C. $46^{\circ}$, D. $88^{\circ}$
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write an equation of the circle with center (-2, 4) and diameter 8.
$(x + 2)^2+(y - 4)^2=16$
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one angle of an isosceles triangle measures 120°. what measures are pos…
A. $30^{\circ}$
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22. what is the image of (-7, -9) after a reflection over the x - axis?…
22. $(-7,9)$ 23. $(2,4)$
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a right triangle has one angle that measures 50°. what is the measure o…
40
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one angle of an isosceles triangle measures 140°. what measures are pos…
20°
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vocab and key ideas midpoint of a segment the of a segment is a point t…
In the diagram to the left, B is the midpoint of AC. A line, ray, or segment that intersects a segment at its midpoint and divides the segment is called the bisector of the segmen…
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find the coordinates of the vertices of the polygon after the given tra…
| Original Point | Translated Point | | ---- | ---- | | $(-3,6)$ | $(3,3)$ | | $(-5,3)$ | $(1,0)$ | | $(-1,3)$ | $(5,0)$ | | $(-3,0)$ | $(3,-3)$ |
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an isosceles triangle has an angle that measures 110°. what measures ar…
B. 35°
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one angle of a right triangle measures 10°. what is the measure of the …
80
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a triangle has interior angle measures of 51°, 66°, and w. what is the …
63
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midpoint of a segment the midpoint of a segment is a point that divides…
The mid - point of a segment is a point that divides the segment into 2 equal parts. A line, ray, or segment that intersects a segment at its mid - point is called the bisector of…
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a triangle has interior angle measures of z, 92°, and 48°. what is the …
$40$
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a triangle has interior angle measures of c, 42°, and 64°. what is the …
$74$
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a triangle has interior angle measures of 102°, s, and 35°. what is the…
43
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midpoint of a segment the mid - point: a mid - point of a segment is a …
1. Point B; segment AC 2. bisector; segment
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rectangle abcd is graphed in the coordinate plane. the following are th…
21
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write the ordered - pair for the point r. the coordinates of point r ar…
(-5, 5)
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the diagram shows a triangle. what is the value of c? c =
64
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the midpoint of a segment is a point that divides the segment into a li…
The midpoint of a segment is a point that divides the segment into two congruent parts. A line, ray, or segment that intersects a segment at its midpoint is said to bisect the seg…
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what additional information is needed to prove that the triangles are c…
∠N≅∠M
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what additional information is needed to prove that the triangles are c…
C. $\angle N\cong\angle M$
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the proof △abc≅△dcb that is shown. given: ∠a≅∠d; cd||ab prove: △abc≅△dc…
AAS
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what additional information could be used to prove that the triangles a…
$\angle A\cong\angle T$ and $AC = TQ = 3.2$cm, $\angle A\cong\angle T$ and $\angle B\cong\angle P$, $\angle A\cong\angle T$ and $\overline{BC}\cong\overline{PQ}$
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which rigid transformation would map △mzk to △qzk? a rotation about poi…
a reflection across the line containing $\overline{ZK}$
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write the ordered - pair for the point r. the coordinates of point r ar…
(3, - 3)
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what additional information could be used to prove that the triangles a…
B. \(\overline{CB}\cong\overline{QM}\), E. \(AB = 2.5\text{cm}\) and \(MQ = 2.5\text{cm}\)
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1. without using your calculator, evaluate each of the following given …
1. - (a) $f(-4)=-5,f(2)=13$ - (b) $g(2)=12,g(-3)=27$ - (c) $h(41)=6,h(14)=3$ 2. - (a) $f(-5)=-7,f(0)=-\frac{1}{2}$ - (b) $g(4)=\frac{3}{4},g(-3)=-\frac{4}{3}$ - (c) $h(3)=51.84,h(…
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given: ∠abc and ∠fgh are right angles; ba||gf; bc≅gh prove: △abc≅△fgh s…
AAS congruence theorem.
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16. point h is located at (-5, -4) on the coordinate plane. point h is …
16. $(5,-4)$ 17. $(-6,6)$
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a side of the triangle below has been extended to form an exterior angl…
\(127\)
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15. if $mangle ecb = 125^{circ}$, $mangle ecd = 2x - 2$, and $mangle dc…
$x = 21$ $m\angle ECD=40^{\circ}$ $m\angle DCB=85^{\circ}$
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28. mathematical connections write an expression for the length of the …
a. $8x - 1$ b. $5y + 20$
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the equation of a circle is given below. identify the center and the ra…
Center: $(0,1)$ Radius: $4$
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a side of the triangle below has been extended to form an exterior angl…
$112$
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symmetry: x - axis y - axis origin none of these
origin
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a side of the triangle below has been extended to form an exterior angl…
\(20\)
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help me solve this view an example get more help. write the ordered - p…
$(0,5)$
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graph 2 symmetry: □x - axis □y - axis □origin □none of these
none of these
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a side of the triangle below has been extended to form an exterior angl…
\(112\)
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a side of the triangle below has been extended to form an exterior angl…
\(36^{\circ}\)
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graph 1 symmetry: □x - axis □y - axis □origin
origin
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analyzing congruence criteria are the triangles congruent? if so, how d…
not enough information given
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3 is there a rigid transformation taking rectangle a to rectangle b? ex…
No, because rigid transformations preserve side - length ratios and a rectangle and a square have different side - length ratios.
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a side of the triangle below has been extended to form an exterior angl…
$23$
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congruence criteria are the triangles congruent? if so, how do you know…
not enough information given
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in the given picture, if mt ⊥ rv, and xs ⊥ xe, identify each pair of an…
10. Vertical 11. Adjacent, Complementary 12. Adjacent, Complementary 13. Adjacent, Supplementary, Linear - pair 14. Adjacent
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during geometry class, students are told that $delta tsrcongdelta usv$.…
Sam is correct.
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a side of the triangle below has been extended to form an exterior angl…
\(x = 63^{\circ}\)
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an airplane flies from city a in a straight line to city b, which is 11…
198 km 514.15 billion
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during geometry class, students are told that δtsr ≅ δusv. marcus state…
Sam is correct.
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plot the point (- 5,-1 1/2) plot the ordered pair
The point \((-5,-1\frac{1}{2})\) is plotted on the coordinate - plane following the above steps.
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analyzing diagrams can you conclude that triangle ghf is congruent to t…
not enough information given
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a side of the triangle below has been extended to form an exterior angl…
\(21\)
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what additional information could be used to prove that δxyz ≅ δfeg usi…
B. $\angle Z\cong\angle G$ and $\angle Y\cong\angle E$ E. $\angle Z\cong\angle G$ and $\overline{XY}\cong\overline{FE}$
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plot the point (-4.5,2.5)
The point (-4.5, 2.9) is plotted on the coordinate plane by moving 4.5 units left on the x - axis and 2.9 units up on the y - axis from the origin.
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(-15.2, 12.2), (5.8, 4.4) (a) plot the points. (b) find the distance be…
(b) $22.4$ (c) $(-4.7,8.3)$
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nate wants to visit his friend mac before going to the park. nates hous…
$(4,5)$
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9. the endpoints of $overline{cd}$ are $c(1, - 6)$ and $d(7,5)$. find t…
$(4,-0.5)$
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a side of the triangle below has been extended to form an exterior angl…
$x = 48$
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sai is rearranging his furniture. he wants his couch to sit along the 2…
A. 6 ft 8 in.
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recall that the sum of all of the angles of a triangle is 180° regardle…
(a) $\angle A$ and $\angle B$ (b) $68^{\circ}$ 6. (4) $122^{\circ}$ 7. $100^{\circ}$ 8. (2) $AC = AD$. Explanation: A point on the perpendicular bisector of a line - segment is eq…
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11. the point n is plotted on the coordinate grid below. plot the point…
Coordinates of M: $(5,-5)$ Coordinates of $M'$: $(5,5)$ When a point is reflected over the x - axis, the y - coordinate changes sign.
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in exercises 3 - 6, use a ruler to measure the length of the segment to…
For exercises 3 - 6: The length of each segment (you need to measure with a ruler). For exercises 7 and 8: A copy of the respective segments can be constructed using the compass a…
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10.(new)two lines intersect. if one angle is 70°, what is it’s vertical…
$70^{\circ}$
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find each measure. 1. fg find the length of $overline{ab}$. 3. a 2. tu …
1. \(FG = 28\) 2. \(TU = 60\) 3. The length of \(\overline{AB}=26\) 4. Assuming relevant length calculation using \(6x + 11\) with \(x = 4\), the length is \(35\)
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fill in the blank so that the resulting statement is true. if two non -…
the same
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(g) 8x - 36 2x+30
$x = 11$
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(f) x + 27 8x
$x = \frac{27}{7}$
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rectangle ijkl is reflected across the y - axis to produce rectangle ij…
$(x,y)\to(-x,y)$
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hexagon cdefgh is reflected across the x - axis to produce hexagon cdef…
$(x, - y)$
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ab is rotated 270° counterclockwise about the origin to produce ab. wri…
$(y, - x)$
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op is rotated 180° clockwise about the origin to produce op. write the …
(-x, -y)
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square bcde is rotated 270° clockwise about the origin to produce squar…
$(y, - x)$
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pentagon fghij is reflected across the y - axis to produce pentagon fgh…
$(x,y)\to(-x,y)$
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which vector goes from (5, 5) to (4, 0)? a. b b. c c. d d. a
D. a
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square abcd is reflected across the y - axis to produce square abcd. wr…
$(x,y)\to(-x,y)$
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consider the following: (3, 9), (9, 3) (a) plot the points. (b) find th…
(b) $6\sqrt{2}$ (c) $(6,6)$ (Note: Plotting the points in part (a) is a visual task that cannot be fully represented in this text - based format. You would go 3 units to the right…
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pentagon nopqr is rotated 270° counterclockwise about the origin to pro…
$(x,y)\to(y, - x)$
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quadrilateral stuv is reflected across the x - axis to produce quadrila…
$(x,y)\to(x, - y)$
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hexagon defghi is rotated 180° clockwise about the origin to produce he…
$(x,y)\to(-x,-y)$
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the coordinate of point x on pq that is 3/4 of the distance from p to q…
$4$
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quadrilateral efgh is rotated 180° counterclockwise about the origin to…
$(x,y)\to(-x,-y)$
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quadrilateral abcd is reflected across the y - axis to produce quadrila…
$(x,y)\to(-x,y)$
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show that the points form the vertices of the polygon. right triangle: …
$d_1 = 2\sqrt{5}$ $d_2 = 2\sqrt{5}$ $d_3 = 2\sqrt{10}$
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partially correct your answer is incorrect. x - intercept: your answer …
x - intercept: 4 y - intercept: 3
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pq is reflected across the y - axis to produce pq 4) write the rule for…
$(x,y)\to(-x,y)$
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(a) find the length of each side of the right triangle. distance betwee…
(a) $d_1 = 5$, $d_2 = 12$, $d_3 = 13$ (b) $d_1^2=25$, $d_2^2 = 144$, $d_1^2 + d_2^2=169$, $d_3^2=169$
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vw is rotated 90° counterclockwise about the origin to produce vw. writ…
$(x,y)\to(-y,x)$
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a△ is reflected across the y - axis in picture a/1. write the rule for …
$(x,y)\to(-x,y)$
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a dog runs out the door and through the neighborhood. it starts at poin…
A. 8 km
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△qrs is rotated 90° clockwise about the origin to produce △qrs. write t…
$(y, - x)$
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10. - / 1 points details find the distance between the points. (round y…
$17.51$
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find the distance between the points. (9, 6), (6, -1)
$\sqrt{58}$
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find the distance between the points. (-12, 6), (3, -2)
$17$
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graph the line y = 7.
Draw a horizontal line passing through the point $(0,7)$ on the $y$-axis. All points on this line have a $y$-coordinate of 7 regardless of the $x$-coordinate.
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4. look at the figure. find the value of x. 65° 60 50 65 55
50
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date: sept22,29 hour: 6 1/2 cameron, arthur, and jamie are playing socc…
20. $29.2$ meters 21. Jamie is closer to Cameron because the distance between Jamie and Cameron ($d_{JC}\approx28.3$ meters) is less than the distance between Arthur and Cameron (…
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question 9 of 25 erin jogs along a path shown by the black vectors in t…
A. Erin jogs 5 blocks west and then 3 blocks south.
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determine the quadrant(s) in which (x, y) could be located. (select all…
quadrant I