Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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20. critique reasoning in a proof, alex wrote the following step: ab = …
The error is that Alex misused the Transitive Property of Congruence. Statements and Reasons: **Statement 1**: \(AB = 7\) and \(BC=7\) **Reason 1**: Given **Statement 2**: \(\over…
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bc is the angle bisector of ∠abd. find m∠abc if m∠abd = 72°. m∠abc =
$36^{\circ}$
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cf bisects ∠bcd. find m∠fcd if m∠bcf=(x - 6)° and m∠bcd=(x + 35)°. x = …
$41^{\circ}$
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question 1 - 16 read the statement. \if a figure is a square, then it i…
If a figure is a rhombus, then it is a square: Converse If a figure is not a square, then it is not a rhombus: Inverse If a figure is not a rhombus, then it is not a square: Contr…
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cf bisects ∠bcd. find m∠fcd if m∠bcf=(x - 6)° and m∠bcd=(x + 35)°. x= m…
$x = 47$ $m\angle FCD=41^{\circ}$
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using the diagram below solve for x. desmos x = 25 x = 16 x = 20 x = 19
x = 16
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mb intersects ∠amc. which of the following statements is true? ∠amb = ∠…
$\angle AMB+\angle BMC=\angle AMC$
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which statements must be true about these angles? choose all that are c…
$\angle1\cong\angle4$ $m\angle2 + m\angle4 + m\angle6=180^{\circ}$ $\angle3\cong\angle5$ $m\angle2 + m\angle3 + m\angle4=180^{\circ}$ $m\angle2 + m\angle3=m\angle5 + m\angle6$
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find the value of \a\ and $overline{ln}$ if m is the midpoint of ln. mn…
a = 12; LN = 48
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bc is the angle bisector of ∠abd. find m∠abc if m∠cbd = 37°. m∠abc =
$37^{\circ}$
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sq bisects ∠rst, and m∠rsq = 3x - 9. write an expression for ∠rst. the …
$6x - 18$
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in the figure, $overrightarrow{gk}$ bisects $angle fgh$. if $mangle fgk…
29
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state a counterexample to the definition below: a figure with four righ…
A rectangle has four right angles
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jl bisects ∠ljk, m∠ljl=(12x - 2)°, and m∠ljk=(8x + 6)°. find m∠ljl. m∠l…
$m\angle IJL = 22^{\circ}$
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question: consider the function y = 2 sin(x) for 0° ≤ x ≤ 360°. 1. grap…
The key points are: x - intercepts $(0^{\circ},0),(180^{\circ},0),(360^{\circ},0)$; maximum point $(90^{\circ},2)$; minimum point $(270^{\circ},-2)$. Plot these points and draw a …
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given a graph, explain how you can identify the x - and y - intercepts.…
To find the x - intercept, look for the points on the graph where y = 0. To find the y - intercept, look for the points on the graph where x = 0.
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18. lee begins to build a model of a barn by arranging the framing stic…
Group 1: \(AB\), \(CD\); Group 2: \(EF\), \(KL\); Group 3: \(IJ\), \(GH\), \(RS\)
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j, k, and l are points on the same segment, and k is between j and l. 1…
14. 9 15. 12 16. \(x = 2\), \(JK = 10\) 17. 14
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use the segment addition postulate to find the missing lengths. 9. ab =…
9. \(AC = 10\) 10. \(AC = 14\) 11. \(BC = 2\) 12. \(BC = 8\) 13. \(AC = 21\)
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state the property of congruence that makes each statement true. the fi…
2. Reflexive Property of Congruence 3. Transitive Property of Congruence 4. Symmetric Property of Congruence 5. Reflexive Property of Congruence 6. Symmetric Property of Congruenc…
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question: consider the function y = 2 sin(x) for 0° ≤ x ≤ 360°. 1. grap…
Points to plot: $(0,0),(90,2),(180,0),(270,-2),(360,0)$ and then draw a smooth sine - curve through them.
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question: consider the function y = 2 sin(x) for 0° ≤ x ≤ 360°. 1. grap…
The x - intercepts are $(0,0),(180,0),(360,0)$, the maximum point is $(90,2)$, and the minimum point is $(270,-2)$. Plot these points and connect them with a smooth curve to graph…
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question: consider the function y = 2 sin(x) for 0° ≤ x ≤ 360°. 1. grap…
The graph of $y = 2\sin(x)$ for $0^{\circ}\leq x\leq360^{\circ}$ has x - intercepts at $(0,0)$, $(180,0)$, $(360,0)$, a maximum point at $(90,2)$ and a minimum point at $(270,-2)$…
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question: consider the function y = 2 sin(x) for 0° ≤ x ≤ 360°. 1. grap…
To graph the function $y = 2\sin(x)$: - X - intercepts: $(0,0),(180,0),(360,0)$ - Maximum point: $(90,2)$ - Minimum point: $(270,-2)$ Plot these points and draw a smooth sine - cu…
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question: consider the function y = 2 sin(x) for 0° ≤ x ≤ 360°. 1. grap…
The key points are $(0,0),(90,2),(180,0),(270,-2),(360,0)$. Plot these points and draw a smooth sine - curve within the interval $0^{\circ}\leq x\leq360^{\circ}$.
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examples 1 and 2 additional practice use the graph to estimate the x - …
For graph 1: x - intercepts: x≈ - 2,x≈2; y - intercept: y≈ - 1; Positive: - 2<x<2; Negative: x < - 2 or x>2. For graph 2: x - intercepts: x≈ - 1,x≈1; y - intercept: y = 0; Positiv…
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what is m∠r? these figures are congruent. what is m∠r?
$34$
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△acb ≅ △stu. what is ba? kilometers submit work it out not feeling read…
55
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nmpo ≅ wxyv. what is yv? inches
16
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these figures are congruent. what is ba? inches
23 inches
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ghif ≅ pqrs. what is m∠i?
\(137\)
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pqro ≅ vwtu. what is m∠t?
108
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△prq≅△xyw. what is m∠y?
$59$
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△fed ≅ △uvw. what is m∠e?
78
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ihgf ≅ mnop. what is m∠h?
97
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these figures are congruent. what is wx? meters
72
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∠abc is a straight angle. what is the value of y? y = ___ ° enter the a…
36
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what is the value of y? y = ___ ° enter the answer check it
18
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what is the value of angle x? x = ___ ° enter the answer check it
\(22.5\)
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the figure is not drawn to scale. ∠abc is a right angle. find m∠cbd. m∠…
$15$
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the figure is not drawn to scale. ∠acb is a right angle. find m∠bcd. a …
\(25\)
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what is the value of angle x? x = ___ ° enter the answer check it impro…
\(45\)
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what is the value of y? y = ___ °.
\(22.5\)
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the figure is not drawn to scale. ∠abd is a right angle. find m∠abc. m∠…
59
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m∠abc = 135°. what is the value of x? x = ___ ° enter the answer
\(27\)
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points that do not form a single straight line when they are connected …
b. Non - collinear points
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given that triangle abc is congruent to triangle pqr, but triangle abc …
a. \(BC = PQ\)
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if a triangle has one angle that is equal to the sum of its other two a…
d. a right triangle
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use the graph to determine the length of segment dh. enter the coordina…
\(d=\sqrt{(-6 - (-12))^{2}+(3 - 2)^{2}}=\sqrt{(6)^{2}+(1)^{2}}=\sqrt{36 + 1}=\sqrt{37}\) The length of segment DH is \(\sqrt{37}\) centimeters.
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if the angles of a triangle are in the ratio 5 : 3 : 7, what type of tr…
A. an acute angled triangle
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john and mohan are of the same age. similarly, mohan and ram are of the…
a. First Axiom
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which of euclids axioms demonstrates the statement that if $x + y = 10$…
b. Second Axiom
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after school garrett and chance walk home. garrett walks 7 blocks east …
Coordinates \((x_1,y_1)\) of point G: \((7,2)\) Coordinates \((x_2,y_2)\) of point C: \((1,9)\) \(d = \sqrt{(1 - 7)^2+(9 - 2)^2}=\sqrt{(-6)^2 + 7^2}=\sqrt{36+49}=\sqrt{85}\) The d…
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what is the second axiom of euclid? a the things which are equal to the…
B. If equals be added to equals, the wholes are equal.
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what are the boundaries of surfaces known as? a surfaces b curves c lin…
B. curves
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determine if the following statement is always true, sometimes true, or…
A. Never
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after school, ethan and latanya walk home. ethan walks 11 blocks east a…
Coordinates \((x_1,y_1)\) of point E: \((11,9)\) Coordinates \((x_2,y_2)\) of point L: \((- 4,8)\) \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(-4 - 11)^2+(8 - 9)^2}=\sqrt{(-15)^…
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use the graph to determine the length of segment go. enter the coordina…
First - blank: \(-10 - 5=-15\) Second - blank: \(-4 - 5=-9\) Third - blank: \(\sqrt{(-15)^2+(-9)^2}=\sqrt{225 + 81}=\sqrt{306}=3\sqrt{34}\approx17.49\) Fourth - blank: \(3\sqrt{34…
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use the graph to determine the length of segment jd. enter the coordina…
First - blank: \(-5 - 3=-8\) Second - blank: \(6 - 4 = 2\) Third - blank: \(d=\sqrt{(-8)^{2}+2^{2}}=\sqrt{64 + 4}=\sqrt{68}=2\sqrt{17}\) Fourth - blank: \(2\sqrt{17}\)
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in a park, which of the following structures is most likely to be a ver…
b. The slide
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use the graph to determine the length of segment em. enter the coordina…
First - box: \(4 - 13=-9\) Second - box: \(-10 - 2=-12\) Third - box: \(\sqrt{(-9)^{2}+(-12)^{2}}=\sqrt{81 + 144}=\sqrt{225}=15\) Fourth - box: \(15\)
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what are axioms considered as? a universal truths in all branches of ma…
a. universal truths in all branches of mathematics
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the angles of a triangle are in the ratio 2 : 4 : 3. what is the measur…
B. $40^{\circ}$
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use the graph to determine the length of segment em. enter the coordina…
Coordinates \((x_1,y_1)\) of point E: \((14,3.5)\) Coordinates \((x_2,y_2)\) of point M: \((5, - 10)\) \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(5 - 14)^2+(-10 - 3.5)^2}=\sqrt…
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what is the second axiom of euclid? a if equals be subtracted from equa…
d. If equals be added to equals, the wholes are equal.
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in triangle abc, ab is equal to ac and ∠b is 50 degrees. what is the me…
B. \(50^{\circ}\)
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use the graph to determine the length of segment or. enter the coordina…
Coordinates \((x_1,y_1)\) of point O: \((- 11,-8)\) Coordinates \((x_2,y_2)\) of point R: \((-1,9)\) \(d=\sqrt{((-1)-(-11))^{2}+(9 - (-8))^{2}}\) \(d=\sqrt{(10)^{2}+(17)^{2}}\) \(…
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use the graph to determine the length of segment or. enter the coordina…
Coordinates \((x_1,y_1)\) of point O: \((- 11,-8)\) Coordinates \((x_2,y_2)\) of point R: \((-1,9)\) \(d=\sqrt{((-1)-(-11))^{2}+(9 - (-8))^{2}}\) \(d=\sqrt{(10)^{2}+(17)^{2}}\) \(…
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john and mohan are of the same age. similarly, mohan and ram are of the…
b. First Axiom
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the coordinates of point e are (9, - 9). the coordinates of point l are…
Coordinates \((x_1,y_1)\) of point E: \((9,-9)\) Coordinates \((x_2,y_2)\) of point L: \((10,10)\) \(d = \sqrt{(10 - 9)^2+(10-(-9))^2}\) \(d=\sqrt{(1)^2+(19)^2}\) \(d=\sqrt{1 + 36…
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the coordinates of point q are (-9, 4). the coordinates of point r are …
Coordinates \((x_1,y_1)\) of point Q: \((- 9,4)\) Coordinates \((x_2,y_2)\) of point R: \((3,-7)\) \(d=\sqrt{(3 - (-9))^{2}+((-7)-4)^{2}}\) \(d=\sqrt{(12)^{2}+(-11)^{2}}\) \(d=\sq…
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after school, dontrell and keiki walk home. dontrell walks 2 blocks wes…
Coordinates \((x_1,y_1)\) of point D: \((- 2,-11)\) Coordinates \((x_2,y_2)\) of point K: \((-7,-10)\) \(d=\sqrt{((-7)-(-2))^{2}+((-10)-(-11))^{2}}\) \(d=\sqrt{(-5)^{2}+1^{2}}\) \…
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after school, carl and santo walk home. carl walks 10 blocks east and 9…
Coordinates \((x_1,y_1)\) of point C: \((10, - 9)\) Coordinates \((x_2,y_2)\) of point S: \((9,-2)\) \(d=\sqrt{(9 - 10)^2+(-2+9)^2}\) \(d=\sqrt{(-1)^2+(7)^2}\) \(d=\sqrt{1 + 49}=\…
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use the graph to determine the length of segment wb. enter the coordina…
First - blank: \(6 - (-11)=17\) Second - blank: \(-10 - 8=-18\) Third - blank: \(\sqrt{17^{2}+(-18)^{2}}=\sqrt{289 + 324}=\sqrt{613}\approx24.76\) Length of segment WB: \(\sqrt{61…
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the coordinates of point i are (1, 5). the coordinates of point r are (…
Coordinates \((x_1,y_1)\) of point I: \((1,5)\) Coordinates \((x_2,y_2)\) of point R: \((5,5)\) \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) \(d=\sqrt{(5 - 1)^2+(5 - 5)^2}\) \(d=\sq…
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what is the length of the unknown leg to the nearest tenth? a 16 10 2.4…
C. 12.5
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a 14 - foot ladder is set up 4 feet from the base of a building. how fa…
13.4 feet
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the measure of ∠b is 68°. what is the measure of its supplementary angl…
C. 112°
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what are the measures of the marked angles? (3x - 8)° (2x + 1)° 19° 27°…
$19^{\circ}$
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consider the points a and b graphed on the coordinate plane. what are t…
\((-1,-2)\)
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use slopes to determine whether the lines are parallel, perpendicular, …
Parallel For the second - part (12):
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graph each pair of lines. use slopes to determine whether the lines are…
9. Neither 10. Perpendicular
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line ds is perpendicular to line tp. line tp is represented by the equa…
$y=-x + 2$
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line rl is represented by the equation y = -x - 2. determine the equati…
$y=x + 5$
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what are tertiary characters? sub characters who play a role that helps…
sub characters who play a role that helps the story come full circle
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use the slope formula to determine the slope of each line. 5. $overline…
5. $0$ 6. $-\frac{5}{6}$ 7. $\frac{4}{3}$ 8. Undefined
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use the slope formula to find the slope of each line. 1. $overline{lm}$…
1. $\frac{1}{2}$ 2. $-1$ 3. Neither 4. Perpendicular
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the figure is not drawn to scale. $overline{ab}$ and $overline{cd}$ are…
\(72\)
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1 mode → par (parametric) 2. x1t = 5cos(t), y1t = 5sin(t). 3 graph → sk…
Vertex: $(3,4)$
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observe the angles. which type of angle is not shown below? right acute…
Question 3: A. Right Question 4: A. Protractor
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which of the following angles is a right angle?
The first option (the angle with the small square at the vertex)
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question 1 which of the following angles is an acute angle?
The second - option (the angle that appears to be less than 90 degrees).
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in progress check for understanding: defining angles not graded directi…
$\{89.1^{\circ},90^{\circ},89.8^{\circ}\}$
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this image has rotational symmetry. what is the smallest number of degr…
30
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question 10 three angles can be put together to make a supplementary an…
60 degrees
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question 8 vertical angles are complementary angles. always true someti…
Question 8: C. Never true Question 9: D. 90 degrees
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the sum of two vertical angles is 140 degrees. what is the measure of o…
1. D. 70 degrees 2. D. There are two pairs of vertical angles.
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question 4 angles a and b are complementary angles. if angle a is twice…
1. C. 60 degrees 2. C. 144 degrees
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question 5 consider the graph. what is the distance of the line segment…
Assume the two - end points of the line segment are \((x_1,y_1)\) and \((x_2,y_2)\). First, count the horizontal and vertical displacements on the graph. Let's say by counting the…
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what is the distance between the points (8, 12) and (16, -3)? 16 17 18 …
B. 17