Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
-
use the diagram below to answer the following: name a ray with endpoint…
1. $\overrightarrow{BA}$ 2. $\overrightarrow{EA}$ 3. $\overrightarrow{XD}$
-
for each line, determine whether the slope is positive, negative, zero,…
Line 1: Positive Line 2: Undefined Line 3: Positive Line 4: Zero
-
dilate segment ab using a scale factor of 4 and the origin, (0, 0), as …
The coordinates of the image of A are $(12,12)$ and the coordinates of the image of B are $(0,12)$.
-
dilate triangle lmn with a scale factor of 1/3 using point p as the cen…
The coordinates of \(L'\) are \((6,\frac{5}{3})\) (coordinates are based on the assumed original coordinates of \(L\) and \(P\) from the grid. If actual coordinates are different,…
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by Side - Side - Angle (SSA), so the triangles cannot be proven congruent.
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by Side - Side - Angle (SSA), so the triangles cannot be proven congruent.
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by Side - Side - Angle (SSA), so the triangles cannot be proven congruent.
-
graphing compound inequalities graph this compound inequality: x < 8.3 …
On the number - line, place an open - circle at 8.3 and draw an arrow to the left. Place an open - circle at 9.8 and draw an arrow to the right.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by having a right - angle and one congruent side, so the triangles are not congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Hypotenuse - Leg (HL), so the triangles can be proven congruent.
-
circle the mixed numbers:
$2\frac{7}{8}$, $1\frac{3}{9}$, $5\frac{3}{1}$, $5\frac{7}{1}$, $8\frac{9}{1}$, $5\frac{2}{5}$, $9\frac{8}{6}$, $2\frac{1}{7}$, $6\frac{5}{9}$, $3\frac{4}{1}$, $7\frac{2}{1}$, $1\…
-
cool down: connect the dots write a congruence statement for each pair …
1. $\triangle PQLM\cong\triangle SFVH$ 2. $\square DECF\cong\square WXUV$ 3. $\triangle ONM\cong\triangle UTE$
-
circle the improper fractions: 4/3, 2 4/3, 7/9, 3/8, 2 9/1, 2/5, 3/4, 7…
$\frac{4}{3},\frac{2}{4/3},\frac{9}{2},\frac{7}{6},\frac{8}{4/1},\frac{9}{8},\frac{8}{3},\frac{7}{6/1},\frac{9}{6},\frac{6}{1}$
-
1. triangle abd is a rotation of triangle cdb around point e by 180°. i…
1. $\angle ADB$ is congruent to $\angle CBD$. 2. Segment $NM$ is congruent to segment $KL$. 3. $\angle QRS$ is congruent to $\angle ZYW$.
-
activity: if we know this, then we know that...and are these parts cong…
1. Translate point A to point D and then rotate around point D to align AB with DE. 2. Segment EF. 3. Corresponding sides of congruent triangles are equal in length. 4. Correspond…
-
graph the line whose x - intercept is 6 and whose y - intercept is 3.
Plot the points (6,0) and (0,3) and draw a line through them.
-
1. a 90 - degree rotation moves the figure ____ quadrant(s) over 2. a 1…
1. 1 2. 2 3. For 90 - degree counter - clockwise rotation: $(x,y)\to(-y,x)$; for 90 - degree clockwise rotation: $(x,y)\to(y,-x)$ 4. $V'(0,2),T'(1,4),R'(4,3)$ 5. $H'(1,-4),N'(3,-1…
-
find the y - intercept and the x - intercept of the line below. click o…
(a) y - intercept: -1 (b) x - intercept: 2
-
find the y - intercept and the x - intercept of the line below. click o…
(a) y - intercept: - 2 (b) x - intercept: 4
-
graph this compound inequality: $x < - 8$ or $xgeq3$ -10 -9 -8 -7 -6 -5…
The graph has an open circle at \(x=-8\) with an arrow pointing left and a closed circle at \(x = 3\) with an arrow pointing right.
-
1. describe the sequence of transformations that will carry nopqfg onto…
1. C. translation, reflection 2. B. Reflection 3. C. reflection, translation 4. A. rotation 180° about the origin 5. A. rotation 90° clockwise about the origin, B. reflection acro…
-
cool down: circular logic conjecture: any 2 circles in the plane are co…
Disagree. Edited conjecture: Any 2 circles in the plane are similar.
-
13. which transformation will carry the figure onto itself. choose all …
A. reflection across the y - axis, C. reflection across the line \(y = 1\)
-
graphing compound inequalities which graphs represents the compound ine…
The second graph (from the top) represents the compound inequality $x\leq\frac{5}{4}$ or $x\geq\frac{5}{2}$ since it has a closed - circle at $1.25$ with an arrow to the left and …
-
12. describe the sequence of transformations that will carry ghij onto …
B. rotation, translation
-
lesson synthesis: points, segments, and zigzags how can we prove they a…
We can use congruence criteria like SAS (Side - Angle - Side), SSS (Side - Side - Side), ASA (Angle - Side - Angle) etc. If we can show that the relevant sides and angles of the t…
-
11. rotate △fev 90° counterclockwise about the point (0,1) to create △f…
| Pre - I | Image | | ---- | ---- | | $F(-3,3)$ | $F'(-2,-2)$ | | $E(-1,4)$ | $E'(-3,0)$ | | $V(1,2)$ | $V'(-1,2)$ |
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by a reflection, so the triangles are congruent.
-
graph this compound inequality: 2.5 ≤ x ≤ 4.5 -5 -4 -3 -2 -1 0 1 2 3 4 …
Drag a closed - circle point to $2.5$, drag another closed - circle point to $4.5$, and shade the region between them on the number line.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Angle - Side (SAS), so the triangles can be proven congruent.
-
10. reflect △fev across the line y = 1 to create △fev. then list the co…
| Pre - I | Image | | ---- | ---- | | $F(x_1,y_1)$ | $F'(x_1,2 - y_1)$ | | $E(x_2,y_2)$ | $E'(x_2,2 - y_2)$ | | $V(x_3,y_3)$ | $V'(x_3,2 - y_3)$ |
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by congruence, so the triangles are congruent.
-
activity 2: zig then zag construct a triangle that is congruent to your…
1. Segments QR and XY are the same length, so they are congruent. Therefore, there is a rigid motion that takes QR to XY. Apply that rigid motion to figure QRS. 2. If necessary, r…
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by congruence, so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Side - Angle (SSA), so the triangles cannot be proven congruent.
-
activity 1: whats the segment? prove the conjecture: if ab is a segment…
The conjecture is proven since by the definition of congruent segments (two segments are congruent if and only if they have the same length), and given that \(AB\) and \(CD\) have…
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Angle - Side (SAS), so the triangles can be proven congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Side - Angle (SSA), so the triangles cannot be proven congruent.
-
circle the proper fractions: types of fractions
$\frac{12}{14},\frac{2}{3},\frac{4}{5},\frac{6}{7},\frac{2}{8},\frac{4}{5},\frac{6}{17},\frac{9}{13},\frac{1}{11},\frac{1}{3},\frac{15}{16},\frac{4}{8},\frac{1}{2},\frac{3}{5},\fr…
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by congruence, so the triangles are congruent.
-
9. graph the images after the composition of transformations. a) reflec…
|Pre - I|$F(0,4)$|$P(2,4)$|$T(2,2)$| |--|--|--|--| |Reflection|$(0,-4)$|$(2,-4)$|$(2,-2)$| |Translation|$(-4,-2)$|$(-2,-2)$|$(-2,0)$|
-
warm up: whats the point? if a is a point on the plane and b is a point…
The claim is True.
-
2. complete the circles with multiplication and dividing expression. 3.…
$\$14450$ (b)
-
deltamath ← back to home triangle proofs no late credit grade: 0% compl…
The triangles are not necessarily congruent.
-
8. graph the images after the composition of transformations. a) reflec…
| |$K$|$N$|$L$| |--|--|--|--| |Pre - I|$(-3,1)$|$(0,-1)$|$(-3,-4)$| |Reflection|$(3,1)$|$(0,-1)$|$(3,-4)$| |Rotation|$(-1,3)$|$(1,0)$|$(4,3)$|
-
are necessarily congruent. in the first three boxes, choose a statement…
We are given two triangles $\triangle DCB$ and $\triangle PNO$. If we assume we have the following congruence - side $\overline{CB}\cong\overline{NO}$ (given), angle $\angle C\con…
-
that they are. the triangles are necessarily congruent. for each of the…
The triangles are necessarily congruent. - First box: $\overline{DC}\cong\overline{ON}$ (Given) - Second box: $\angle C\cong\angle N$ (Given) - Third box: $\triangle BCD$ and $\tr…
-
2. what are the coordinates of b after the following composition of tra…
B. (4,0)
-
the triangles are necessarily congruer for each of the first three boxe…
The triangles are not necessarily congruent.
-
the triangles are necessarily congruent. for each of the first three bo…
No
-
e. the distance from the tip of a slice of pizza to the crust is 7 in. …
\(24 + 6\pi\approx42.84\) units
-
a bulldozer clears a rectangular piece of land of sides 1.732 km × 1.5 …
$3.711428571\times 10^{1}$ km²
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by Angle - Angle - Angle (AAA), so the triangles cannot be proven congruent.
-
1. describe the sequence of transformations that will carry abcde onto …
A. reflection, translation
-
question determine the relationship between the two triangles and wheth…
1. Relationship: Congruent by ASA (assuming the marks indicate one pair of equal sides and two pairs of equal angles). 2. Conclusion: The triangles are congruent.
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by congruence, so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The relationship is congruent by ASA (assuming one - side and two - included angles are marked congruent as indicated by the markings on the triangles), so the triangles are congr…
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by a rotation, so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by a reflection, so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Angle - Side (SAS), so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by a reflection, so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Angle - Side (SAS) congruence criterion, so the triangles are congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Angle - Side (SAS), so the triangles CAN be proven congruent.
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by Side - Angle - Side (SAS) but CANNOT be proven congruent.
-
map on the right to answer the following questions. how far must you tr…
$4\sqrt{5}\approx8.94$ 2.
-
a triangle abc is dilated to obtain triangle abc as shown on the coordi…
The scale factor of the dilation is 2, and the coordinates of the center of the dilation are $(2,-2)$
-
2. find the distance cd of c(-6, 4) and d(-3, -2)
$3\sqrt{5}$
-
construction: the image below shows the beginning of a staircase. calcu…
0.7
-
16. drag and drop the numbers into each of the boxes to complete the se…
The scale factor of the dilation is \(2\), and the coordinates of the center of the dilation are \((2,-2)\)
-
in △abc, line segments ac ≅ bc and m∠bca = 70°. 15. what is the measure…
C. $55^{\circ}$
-
in the figure, line ab intersects line cd to form four angles. the tabl…
The steps and reasons to complete the proof are as follows: | Steps | Reasons | |--|--| | 1. $m\angle1 + m\angle3 = 180^{\circ}$, $m\angle2 + m\angle3=180^{\circ}$ | Linear - pair…
-
triangle abc is transformed to obtain triangle abc as shown. 13. drag t…
Step 1: Counterclockwise rotation by 90° about the origin Step 2: Translation 1 unit down
-
12. in △mno and △pqr, ∠mno≅∠pqr and no≅qr. what additional congruence i…
B. $\overline{MN}\cong\overline{PQ}$
-
11. if △abc~△pqr, which statement describes cos c and cos r? remember c…
A. The values of the cos of $\angle C$ and the cos of $\angle R$ are equal.
-
learning target: find the distance of two poi 1. find the distance ab o…
$2\sqrt{109}$
-
10. what is the volume of the cone shown? (use π = 3.14) a. 130,833.33 …
D. $32,708.33$ $cm^{3}$
-
determine the altitude (height) of the plane in the image below. note: …
600 m
-
7. what is the value of x? (x + 23)° (2x + 4)° a 19 b 21 c 51 d 74
A. 19
-
talia is packing a moving box. she has a square - framed poster with an…
Yes, the poster will lie flat in the box because the volume of the box (33 cubic feet) is larger than the volume of a cube with side - length equal to the side - length of the squ…
-
10. what is the volume of the cone shown? (use π = 3.14) a. 130,833.33 …
D. $32,708.33$ $cm^{3}$
-
9. triangle abc has vertices at a (3, 5), b (5, 7) and c (7, 5). lisa b…
We first need to find the lengths of the sides of the triangle using the distance - formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For side \(AB\) with \(A(3,5)\) and \(B(5,7)\…
-
talía is packing a moving box. she has a square - framed poster with an…
Yes, because if the side of a cube equal to the side of the poster (4 feet) has a volume of 64 cubic feet which is less than the volume of the box (68 cubic feet), meaning the box…
-
6. maria claims \all isosceles triangles are similar.\ which statement …
B. Maria's claim is incorrect because the angles of isosceles triangles are not always congruent.
-
in the figure shown, △pqr~△dfe. 7. which equation can be used to find t…
C. $\frac{x + 1}{6}=\frac{x+3}{x + 6}$
-
6. maria claims all isosceles triangles are similar. which statement be…
A. Maria's claim is incorrect because isosceles triangles have two equal sides, and similar triangles cannot have equal sides.
-
square abcd can be mapped onto the square pqrs by a dilation about the …
A. 4
-
talita is packing a moving box. she has a square - framed poster with a…
Yes, the poster will lie flat in the box because the side - length of the box is greater than the side - length of the square poster.
-
1. using the figure below to prove that vertical angles, ∠1 and ∠3, are…
C. Say that \(m\angle1 + m\angle2=m\angle2 + m\angle3\) because of the Angle - Addition Postulate
-
a company is making building blocks. what is the length of each side of…
$1\mathrm{ft}$
-
dition postulate to find a missing angle. 11. given: ∠bac = 2x + 11 ∠ca…
$m\angle BAC = 35^{\circ}$
-
jeremy is using the figure below to prove that vertical angles, ∠1 and …
A. Say that \(m\angle1 + m\angle2=180^{\circ}\) and \(m\angle2 + m\angle3 = 180^{\circ}\) because of the Definition of Supplementary Angles Discipline: Mathematics Sub - field: Ge…
-
jeremy is using the figure below to prove that vertical angles, ∠1 and …
B. Say that \(m\angle1 + m\angle2+m\angle3 = 180^{\circ}\) because of the Angle - Addition Postulate
-
1. a quadrilateral abcd is translated to the right by 2 units to obtain…
B. The length of \(\overline{A'B'}\) must be equal to the length of \(\overline{AB}\)
-
a company is making building blocks. what is the length of each side of…
$1$
-
learning target: apply the angle ad given: m∠abc = 3x + 3 m∠cbd = 6x + …
$m\angle ABC = 15^{\circ}$, $m\angle CBD=25^{\circ}$
-
learning target: apply the angle addition postulate to find a missing a…
\(m\angle ABC = 15^{\circ}\), \(m\angle CBD=25^{\circ}\)
-
in the figure, ∠6 and ∠3 are ______. consecutive interior angles altern…
alternate interior angles
-
in the figure, ∠1 and ∠2 are ________. corresponding angles alternate i…
alternate exterior angles
-
how much air is inside an 24 - inch wide beach ball? leave your answer …
$2304$
-
the rectangular prism pictured below has height 7 cm, length 10 cm, and…
$310$