幾何
三角形、円、座標幾何、証明問題。
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can $\\triangle abe$ be proved congruent to $\\triangle cde$ by the sid…
\( \angle AEB \cong \angle CED \), \( AE \cong CE \), \( BE \cong DE \)
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the surry county sheriffs patrol route starts in coby. the composition …
The sheriff drives 20 miles left and 10 miles up from Coby to Byder. Then she drives 40 miles right and 50 miles down from Byder to the next patrol location.
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select the statement that most accurately describes the given informati…
Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
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select the statement that most accurately describes the given informati…
A. Three sides of one triangle are congruent to three sides of another triangle.
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10. in the kite shown, ( mangle adc = 105^circ ) and ( mangle dab = 100…
\( 50^\circ \)
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question 7: an equilateral triangle has a side length of 10 units. what…
\( 25\sqrt{3} \) square units (or typed as 25sqrt3)
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question 13 (technology required) the sun is 62 degrees above the horiz…
\(22.6\) (or \(22.57\) depending on precision, but nearest tenth is \(22.6\))
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question 11 find the missing side in each triangle using any method. ch…
\(x = 4\) units, \(y = 15\) units
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segment ac is on the line of reflection, so it is taken to itself, maki…
- Segment \(AB\) reflects to segment \(\boldsymbol{AD}\) - Segment \(CD\) is a reflection of segment \(\boldsymbol{CB}\) - Angle \(DAC\) is a reflection of angle \(\boldsymbol{BAC…
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question 9 select all true statements. image of a right triangle with r…
b. \(AC\) is 13 units, d. \(\sin(\alpha)=\frac{12}{13}\), e. \(\theta=\tan^{-1}(\frac{5}{12})\)
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y is the midpoint of \\(\\overline{wx}\\). complete the proof that \\(\…
\( \overline{VY} \cong \overline{VY} \) (or \( VY = VY \))
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question 3 (technology required) find the missing side length and angle…
BC ≈40.8, ∠B≈59.0°, ∠C≈31.0° (For BC: approximately 40.8, angle B approximately 59 degrees, angle C approximately 31 degrees)
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a 10-foot-tall ladder is placed against a wall so that the top of the l…
4.4
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$\\pi$ radians = $180^\\circ$. use this information along with the diag…
\(\frac{5\pi}{3}\) matches \(300^\circ\), \(\frac{\pi}{6}\) matches \(30^\circ\), \(\frac{3\pi}{4}\) matches \(135^\circ\), \(\frac{11\pi}{6}\) matches \(330^\circ\)
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the distance between the points (-4, -3) and (5, y) is 9√2. use the dis…
6 (or -12, here we choose 6 as a possible value)
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question 1-15 describe the transformation algebraically that takes quad…
The transformation is given by the rule \( (x,y)\to(-x,-y) \) (assuming the correct option is the second or third option with this rule, based on the coordinate mappings of the po…
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question 1-14 triangle abc with coordinates a(-3,0), b(-1,0), and c(-3,…
\((x,y)\to(x - 3,y + 2)\), Triangle ABC translates 3 units to the left and 2 units up.
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question 1-11 find the coordinates of point p along the directed line s…
(8, 2)
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question 1-9 in △pqr, pq = qr, m∠p = (2x - 26)°, and m∠r = (x + 17)°. c…
isosceles, acute, equilateral (select these options as they apply: isosceles because \( PQ = QR \), acute because all angles \( 60^\circ \), equilateral because all angles \( 60^\…
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)) ( overline{fg} perp overline{eg} ). complete the proof that ( mangle…
To complete the proof: 1. **Reason for \( \overline{FG} \perp \overline{EG} \)**: Definition of Perpendicular Lines (perpendicular lines form a \( 90^\circ \) angle). 2. **Reason …
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question 1-6 which additional statements are needed to prove \\(\\trian…
The additional statements needed are $\boldsymbol{\angle C\cong\angle M}$, $\boldsymbol{\overline{LK}\cong\overline{AB}}$, $\boldsymbol{\overline{KM}\cong\overline{BC}}$ (dependin…
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one of the angles of △abc has a measure of 57°. one of the angles of △r…
\(40^\circ\)
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2. if \\( \\triangle rst \\) is an equilateral triangle, find \\( x \\)…
\(x = 8\), and each side measures \(74\).
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performance matters question 5 of 26 submit test 53.2526.q2.ma.geom (im…
$\triangle ABC\cong\triangle DEF$ using Side - Angle - Side triangle congruence postulate.
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performance matters question 3 of 26 53.2526.q2 submit test question 1-…
D. A pair of same - side interior angles formed by parallel lines and a transversal
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question 1-2 a true statement is given. \if two sides and the included …
The fourth option (the one stating: "If two sides and the included angle of one triangle are not congruent to two sides and the included angle of a second triangle, then the trian…
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triangle abc can be mapped onto triangle xyz by a represented by (x,y) …
(Assuming typical options for the dropdowns, for the last part about similarity: "is", and for transformations: first "dilation" then "translation", and the mappings. But based on…
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a true statement is given \if three sides of one triangle are congruent…
If one triangle is congruent to a second triangle, then three sides of the one triangle are congruent to three sides of the second triangle
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fj || gi. complete the proof that m∠hgj = m∠f + m∠j without using the t…
Additive Property of Angle Measure
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question 1-10 what are the coordinates of the centroid of △pqr with ver…
\((0, 4)\)
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fj || gi. complete the proof that m∠hgj = m∠f + m∠j without using the t…
1. Reason for statement 1: Given 2. Reason for statement 2: Corresponding Angles Postulate 3. Reason for statement 3: Alternate Interior Angles Theorem 4. Reason for statement 4: …
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performance matters question 9 of 10 submit test find the value for x. …
11.67
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problem 5 these two lines are parallel. write an equation for each.
The equations of the two parallel lines are \(y = 0.8x\) (or \(y=\frac{4}{5}x\)) and \(y=0.8x - 3.2\) (or \(y=\frac{4}{5}x-\frac{16}{5}\)).
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classifying triangles (in the coordinate plane) classify: 21. 22. 23. f…
- **Problem 21**: Isosceles Triangle (two sides \(2\sqrt{17}\), one side \(6\sqrt{2}\)) - **Problem 22**: Scalene Triangle (all sides \(\sqrt{41}\), \(\sqrt{85}\), \(\sqrt{130}\) …
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section b: linear problem 3 what is the weight of a square if a triangl…
El peso del cuadrado es 8 gramos. ### Problem 4a
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formation shown in the diagram. 6.
The figure undergoes a 90 - degree clockwise (or appropriate) rotation (specific transformation details depend on exact coordinates, but the geometric transformation is rotation).
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19. proof prove that the green triangles in the jamaican flag are congr…
The green triangles (e.g., \(\triangle ADE\) and \(\triangle CBE\)) are congruent by the ASA congruence criterion (using \(AD\parallel BC\) for alternate interior angles, \(E\) as…
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12. 15in 20in 18in 13. 14. 5ft 97° 5ft if \\( \\overline{pr} \\) bisect…
For Triangle 12 (15in, 18in, 20in): Acute Scalene Triangle For Triangle 13 (Right Triangle): Right Scalene Triangle For Triangle 14 (5ft, 5ft, 97°): Obtuse Isosceles Triangle For …
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classifying triangles (by sides) 3 congruent sides 2 congruent sides no…
6. Isosceles 7. Isosceles 8. Isosceles (Note: The exact classification depends on the congruent side markings in the diagram. If the markings indicate two congruent sides for each…
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classifying triangles (by angles) classify each triangle in the diagram…
1. $\triangle CDE$: Obtuse Triangle 2. $\triangle BCE$: Acute Triangle 3. $\triangle ABE$: Acute Triangle 4. $\triangle BDE$: Right Triangle 5. $\triangle CFE$: Right Triangle
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50 which equation can be used to find the missing angle? a) $46 + 32 = …
c) \(x + 78 = 180\)
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match the following triangles with their correct definition. acute tria…
- Acute Triangle: Has 3 acute angles - Scalene Triangle: Has no equal sides - Isosceles Triangle: Has at least 2 equal sides - Equilateral Triangle: All sides are the same length …
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48. triangle image with two equal sides marked and two base angles mark…
b) Isosceles, acute ### Question 49
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46. what kind of triangle is this? (image of a green triangle with angl…
a) right ### Question 47
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in exercises 15 and 16, use the information given in the diagram to wri…
By proving \( \triangle FGJ \cong \triangle HGK \) (SAS) and \( \triangle JML \cong \triangle KMN \) (SAS), then using segment addition and substitution, we show \( FL = HN \), so…
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for each pair of figures below, choose how they are related. (figures i…
First Pair: Rotation Second Pair: Reflection Third Pair: Translation Fourth Pair: Translation
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in exercises 13 and 14, write a proof to verify that the construction i…
The construction is valid as shown by proving triangle congruences (SSS, SAS) and using CPCTC to show right angles, confirming the perpendicular line through \( P \) to \( AB \).
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central & inscribed angles practice directions: find the value of each …
For Problem 1: \(x = \boxed{90}\) (and similar solutions for other problems following the above steps)
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(15) determine the correct congruence. which of the following triangle …
(ת) \( \triangle ARP \cong \triangle ASG \)
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a triangular shelf has an area of 132 in² with a base of 24 in. use the…
11 in
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vocabulary and core concept check 1. complete the sentence ______ parts…
Corresponding
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graph the inequality on the axes below. x - 2y < -4
The graph has a dashed line \(y=\frac{1}{2}x + 2\) (passing through \((0,2)\) and \((2,3)\) etc.) and the region above the line is shaded.
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35. problem solving a boat is traveling parallel to the shore along \\(…
$SL$ is 2.1 miles.
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match the inequality below to the correct graph. $6 \\leq x$ a <----|--…
A. The graph with a closed circle at 5 and an arrow pointing to the right.
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in the diagram are isosceles triangles with congruent vertex angles. 25…
The yellow and purple triangles are isosceles with congruent vertex angles (given the wheel's triangles have congruent vertex angles) and equal leg lengths (radii of the circular …
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modeling with mathematics in exercises 25–28, use the diagram based on …
The yellow and purple triangles are congruent by the SAS congruence criterion. All 12 triangles are isosceles (two equal legs, as radii of the circle) with congruent vertex angles…
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21. finding a pattern in the pattern shown, each small triangle is an e…
The areas of the first four triangles are 1 square unit, 4 square units, 9 square units, and 16 square units. ### Part (a)
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19. error analysis describe and correct the error in finding the length…
The error is misapplying the Isosceles Triangle Theorem (matching the wrong sides to the congruent angles). The correct length of $BC$ is $5$ (since $BC$ is opposite $\angle A$ an…
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construction in exercises 17 and 18, construct an equilateral triangle …
The equilateral triangle with side length 3 inches is constructed as described above. (Note: Since this is a construction problem, the final answer is the constructed triangle. If…
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triangle efg is transformed to create triangle efg. which transformatio…
rotation (the option labeled "rotation")
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is there a series of rigid transformations that could map δrst to δxyt?…
Yes, \( \triangle RST \) can be reflected across the line containing \( RT \) and then rotated about \( T \) so that \( S \) is mapped to \( Y \).
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triangle abc has the angle measures shown. m∠a = (2x)° m∠b = (3x)° m∠c …
B. \(m\angle B = 60^\circ\) (assuming the second option is labeled B; adjust identifier based on original options, but the correct statement is \(m\angle B = 60^\circ\))
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which composition of similarity transformations maps δlmn to δlmn? a di…
a dilation with a scale factor greater than 1 and then a translation (the option corresponding to this description in the choices, likely the last or relevant one with dilation >1…
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angle klm and angle mln are a linear pair. ray lr is to be added to the…
3. Angles RLN and KLM would be a linear pair.
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the proof that $\\triangle abc \\cong \\triangle cda$ is shown. given: …
SSS congruence theorem
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what is the length of line segment lj? 9 units 12 units 15 units 18 uni…
15 units
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myra took a picture of the sky one afternoon when two jet airplanes app…
The three true options are: - \( m\angle3 = m\angle6 = 98^\circ \) - \( m\angle4 = m\angle8 = 82^\circ \) - \( m\angle5 = m\angle8 = 82^\circ \)
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the triangles are congruent by the sss congruence theorem. which rigid …
The option "reflection, then translation" (the second option among the choices, with text "reflection, then translation").
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what is the volume of this cone? round your answer to the nearest hundr…
\( 2412.74 \)
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11. modeling with mathematics the dimensions of a sports pennant are gi…
\(x = 79\), \(y = 22\)
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in exercises 7–10, find the value of x. (see example 2.) 7. a / \\ b---…
\(x = 12\) ### Problem 8:
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in exercises 3–6, copy and complete the statement. state which theorem …
s: 3. If \( \overline{AE} \cong \overline{DE} \), then \( \angle A \cong \angle D \) (Theorem: Isosceles Triangle Theorem) 4. If \( \overline{AB} \cong \overline{EB} \), then \( \…
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34. which set of words includes domain - specific vocabulary that would…
The option with "acute, equilateral, diameter" (the third option in the list of choices)
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34. which set of words includes domain - specific vocabulary that would…
The option with "acute, equilateral, diameter" (the third option from the left, or the option with these three words)
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5. which phrase best describes comparative literature? ○ a tool for eva…
The second option (the second circle): a field of study in which people analyze how the written works of various cultures are similar and different
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select the correct answer. circle o is represented by the equation ((x …
B. 4
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select the correct answer. which point lies on the circle represented b…
A. (20, - 3)
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4. triangles sut and abc are similar. select all proportionalities by p…
The correct proportions are: - \( \frac{BC}{AB} = \frac{SU}{TU} \) (check this box) - \( \frac{ST}{SU} = \frac{AC}{BC} \) (check this box)
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3) a 20 b, 68, 64, d 24 c; e d, b a; dilation factor \\(\\frac{1}{2}\\)
If we take AB = 20, dilated length is 10; DC = 24, dilated is 12; BC = 64, dilated is 32; AD = 68, dilated is 34. (Depending on the corresponding side, but the dilation factor is …
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the city council is planning to construct a park on north street that h…
B. at the center of the inscribed circle of the park
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select the correct answer from each drop - down menu. trapezoid pqrs be…
Trapezoid PQRS \(\boldsymbol{\text{can}}\) be inscribed in a circle because the \(\boldsymbol{\text{sum of each pair of opposite angles is } 180^\circ}\) (or "base angles are supp…
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quadrilateral bcde is inscribed in circle a as shown. what is m∠e? a. 8…
B. \(96^\circ\)
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in jaden’s yard, there is a triangular garden patch. he wants to plant …
B. in the center of the circumscribed circle of the triangle
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giarna is constructing a circle that passes through all three vertices …
A. inside the triangle
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drag each tile to the correct box. consider the given circles. order th…
Sector A, Sector C, Sector B
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in a circle centered at point o, the ratio of the area of sector aob to…
D. 3.77
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the minute hand on a clock is 6 inches long. between 1:15 p.m. and 1:40…
C. 15.71 inches
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a water sprinkler has a range of 5 meters as shown. the jet of water fr…
C. 18.5 square meters
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45. what kind of triangle is this? a) obtuse b) acute c) right
a) obtuse
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select the correct answer. points a, b, and c are located on a circle, …
C. $176^\circ$
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type the correct answer in each box. use numerals instead of words. if …
For \(m\angle BDA\): \(55\) For \(m\angle BCA\): \(70\)
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given that qm = 15 units, sm = 10 units, and rm = 18 units, what is the…
A. 12 units
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select the correct answer. what is the value of x in the given figure? …
D. 18
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family of lines separate the graph paper into 4 sections and then graph…
### Family E (Horizontal Lines) - Slope: \( 0 \) for all equations (\( y = 1,y=-7,y = 5,y=-3 \)) - Y - intercept: \( 1,-7,5,-3 \) respectively - Similarities: All are horizontal (…
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solve for x a) -10 c) -8 b) -12 d) -5 solve for x a) 85° c) 45° b) -88 …
For the first problem (solve for x in the triangle with angles \(70^\circ\), \(65^\circ\), \(x + 53\)): \(\boxed{-8}\) (corresponding to option c). For the triangle type problem: …
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1 select the correct answer from each drop-down menu. segment \\(\\over…
First drop - down: perpendicular to; Second drop - down: tangent to
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Question was provided via image upload.
1. **Step 1: Set up the coordinate system** - Draw a vertical line (north - south) and a horizontal line (east - west) intersecting at a point (the starting point of the plane's j…
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solve for x. (first triangle: angles x + 59, x + 51, 84°) options for f…
For the triangle with angles \(70^\circ\), \(65^\circ\), \(x + 53\): \(x=-8\) (option c) For the triangle type (angles \(39^\circ\), \(50^\circ\), \(91^\circ\)): obtuse (option a)…
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38. exterior angle theorem ∠1 + ∠2 = ___ a) 180 b) 90 c) <4 d) <3 the e…
d) 45 ### Problem 41: Find the missing angle
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33 solve for x a) 36 b) 86 c) 77 d) 76 34 solve for x a) 65 b) 60 c) 40…
b) 86 ### Problem 34: Solve for \( x \)