Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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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.
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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.
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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.
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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\…
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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. $\triangle ONM\cong\triangle UTE$
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circle the improper fractions: 4/3, 2 4/3, 7/9, 3/8, 2 9/1, 2/5, 3/4, 7…
$\frac{4}{3},\frac{2}{4/3},\frac{9}{2},\frac{7}{6},\frac{8}{4/1},\frac{9}{8},\frac{8}{3},\frac{7}{6/1},\frac{9}{6},\frac{6}{1}$
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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 $\angle ZYW$.
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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…
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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.
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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…
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find the y - intercept and the x - intercept of the line below. click o…
(a) y - intercept: -1 (b) x - intercept: 2
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find the y - intercept and the x - intercept of the line below. click o…
(a) y - intercept: - 2 (b) x - intercept: 4
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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.
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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…
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cool down: circular logic conjecture: any 2 circles in the plane are co…
Disagree. Edited conjecture: Any 2 circles in the plane are similar.
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13. which transformation will carry the figure onto itself. choose all …
A. reflection across the y - axis, C. reflection across the line \(y = 1\)
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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 …
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12. describe the sequence of transformations that will carry ghij onto …
B. rotation, translation
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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…
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11. rotate △fev 90° counterclockwise about the point (0,1) to create △f…
| Pre - I | Image | | ---- | ---- | | $F(-3,3)$ | $F'(-2,-2)$ | | $E(-1,4)$ | $E'(-3,0)$ | | $V(1,2)$ | $V'(-1,2)$ |
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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.
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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.
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10. reflect △fev across the line y = 1 to create △fev. then list the co…
| Pre - I | Image | | ---- | ---- | | $F(x_1,y_1)$ | $F'(x_1,2 - y_1)$ | | $E(x_2,y_2)$ | $E'(x_2,2 - y_2)$ | | $V(x_3,y_3)$ | $V'(x_3,2 - y_3)$ |
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determine the relationship between the two triangles and whether or not…
The two triangles are related by congruence, so the triangles are congruent.
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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…
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determine the relationship between the two triangles and whether or not…
The two triangles are related by congruence, so the triangles are congruent.
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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.
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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…
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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.
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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.
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circle the proper fractions: types of fractions
$\frac{12}{14},\frac{2}{3},\frac{4}{5},\frac{6}{7},\frac{2}{8},\frac{4}{5},\frac{6}{17},\frac{9}{13},\frac{1}{11},\frac{1}{3},\frac{15}{16},\frac{4}{8},\frac{1}{2},\frac{3}{5},\fr…
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determine the relationship between the two triangles and whether or not…
The two triangles are related by congruence, so the triangles are congruent.
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9. graph the images after the composition of transformations. a) reflec…
|Pre - I|$F(0,4)$|$P(2,4)$|$T(2,2)$| |--|--|--|--| |Reflection|$(0,-4)$|$(2,-4)$|$(2,-2)$| |Translation|$(-4,-2)$|$(-2,-2)$|$(-2,0)$|
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warm up: whats the point? if a is a point on the plane and b is a point…
The claim is True.
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2. complete the circles with multiplication and dividing expression. 3.…
$\$14450$ (b)
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deltamath ← back to home triangle proofs no late credit grade: 0% compl…
The triangles are not necessarily congruent.
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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|$(-1,3)$|$(1,0)$|$(4,3)$|
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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…
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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…
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deltamath back to home triangle proofs no late credit grade: 0% complet…
The triangles are necessarily congruent. For the second - given statement: $\angle C\cong\angle N$ (assuming the marked angles in the diagram are the ones to be used for the AAS c…
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2. what are the coordinates of b after the following composition of tra…
B. (4,0)
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the triangles are necessarily congruer for each of the first three boxe…
The triangles are not necessarily congruent.
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the triangles are necessarily congruent. for each of the first three bo…
No
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e. the distance from the tip of a slice of pizza to the crust is 7 in. …
\(24 + 6\pi\approx42.84\) units
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a bulldozer clears a rectangular piece of land of sides 1.732 km × 1.5 …
$3.711428571\times 10^{1}$ km²
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1. describe the sequence of transformations that will carry abcde onto …
A. reflection, translation
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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…
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determine the relationship between the two triangles and whether or not…
The two triangles are related by a rotation, so the triangles are congruent.
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determine the relationship between the two triangles and whether or not…
The two triangles are congruent by the Side - Angle - Side (SAS) congruence criterion.
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1. john runs at different speeds as part of his training program. the g…
C ### 2.
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map on the right to answer the following questions. how far must you tr…
$4\sqrt{5}\approx8.94$ 2.
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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 $(2,-2)$
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2. find the distance cd of c(-6, 4) and d(-3, -2)
$3\sqrt{5}$
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construction: the image below shows the beginning of a staircase. calcu…
0.7
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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 \((2,-2)\)
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in △abc, line segments ac ≅ bc and m∠bca = 70°. 15. what is the measure…
C. $55^{\circ}$
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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…
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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
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12. in △mno and △pqr, ∠mno≅∠pqr and no≅qr. what additional congruence i…
B. $MN\cong PQ$
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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.
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learning target: find the distance of two poi 1. find the distance ab o…
$2\sqrt{109}$
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determine the altitude (height) of the plane in the image below. note: …
600 m
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7. what is the value of x? (x + 23)° (2x + 4)° a 19 b 21 c 51 d 74
A. 19
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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…
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10. what is the volume of the cone shown? (use π = 3.14) a. 130,833.33 …
D. $32,708.33$ $cm^{3}$
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9. triangle abc has vertices at a(3, 5), b(5, 7) and c(7, 5). lisa beli…
A. Because $AB = 2\sqrt{2}$ units, $BC = 2\sqrt{2}$ units and $AC = 4$ units.
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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…
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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.
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in the figure shown, △pqr~△dfe. 7. which equation can be used to find t…
C. $\frac{x + 1}{6}=\frac{x+3}{x + 6}$
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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.
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square abcd can be mapped onto the square pqrs by a dilation about the …
The scale factor of the dilation is \(4\), so the answer is A. 4.
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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
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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.
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square abcd can be mapped onto the square pqrs by a dilation about the …
A. 4
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a company is making building blocks. what is the length of each side of…
$1\mathrm{ft}$
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dition postulate to find a missing angle. 11. given: ∠bac = 2x + 11 ∠ca…
$m\angle BAC = 35^{\circ}$
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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…
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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
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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 \(\overline{AB}\)
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a company is making building blocks. what is the length of each side of…
$1$
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learning target: apply the angle ad given: m∠abc = 3x + 3 m∠cbd = 6x + …
$m\angle ABC = 15^{\circ}$, $m\angle CBD=25^{\circ}$
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learning target: apply the angle addition postulate to find a missing a…
\(m\angle ABC = 15^{\circ}\), \(m\angle CBD=25^{\circ}\)
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in the figure, ∠6 and ∠3 are ______. consecutive interior angles altern…
alternate interior angles
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in the figure, ∠1 and ∠2 are ________. corresponding angles alternate i…
alternate exterior angles
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how much air is inside an 24 - inch wide beach ball? leave your answer …
$2304$
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the rectangular prism pictured below has height 7 cm, length 10 cm, and…
$310$
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what are the vertex and the axis of symmetry of the parabola shown in t…
The vertex is \((0, - 1)\), and the axis of symmetry is \(x = 0\). So the correct option is: The vertex is \((0, - 1)\), and the axis of symmetry is \(x = 0\).
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what portion of the figure below is not shaded? write your answer as a …
30%
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in exercises 7 and 8, sketch a diagram of the description. 7. $overline…
For Exercise 7: A diagram with three line - segments intersecting at two points. For Exercise 8: A diagram with two perpendicular planes, a line on their intersection, and the mid…
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what is the perimeter of the rectangle shown on the grid? units
20
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find the distance between the points (3, 8) and (9, 1). round decimals …
$9.2$
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the area of a rectangle is $(x^{3}-5x^{2}+3x - 15)$, and the width of t…
D. $x - 5$
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etween the points (10, 7) and (2, 2). the nearest tenth.
$9.4$
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a circle is inscribed in a square. find the circles area as a function …
A. $f(x)=\frac{\pi x^{2}}{64}$
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graph the line that passes through the points (3, -7) and (-3, 5) and d…
The equation of the line is $y=-2x - 1$
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incorrect your answer is incorrect. graph the solution to the inequalit…
On the number - line, place open circles at \(-3\) and \(3\), and shade the region between them.
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notes: proving triangles congruent name and mark all of the correspondi…
Corresponding angles: $\angle A=\angle D$, $\angle B=\angle E$, $\angle C=\angle F$. Corresponding sides: $AB = DE$, $BC=EF$, $AC = DF$.
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in exercises 1 - 6, use the diagram to write an example of the postulat…
1. For example, for points $D$ and $E$, there is a line passing through them. 2. Line $\overleftrightarrow{EF}$ contains points $E$ and $F$. 3. Lines may intersect at a single poi…
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for # 7 - 10, mark the triangles and complete the congruence statements…
7. $\angle T\cong\angle E$, $\overline{EG}\cong\overline{TV}$, $\angle F\cong\angle U$ 8. $\angle V\cong\angle H$, $\angle IGH\cong\angle UVW$, $\overline{WV}\cong\overline{HI}$ 9…
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solve the inequality and graph the solution. 4(g - 6) < 8 plot the endp…
The solution of the inequality is $g < 8$. On the number - line, we plot an open circle at 8 (since the inequality is strict, $g$ cannot equal 8) and draw a ray to the left of 8.