Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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find the area of the shaded figure. the area is (simplify your answer.)
\( y^2 + 38y + 361 \) (or \( (y + 19)^2 \))
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2 the following statements (1) to (4) represent the conditions for quad…
\( \angle B=\angle D \) #### (2)
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1 find the length of a, b, and c and the measure of ∠x, ∠y, and ∠z in t…
\( a = 6 \) cm, \( b = 5 \) cm, \( \angle x = 65^\circ \) ### Problem 1 (2)
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the area of a rectangle, ( a = l cdot w ) is represented by the express…
A. \(2x^{5}y^{8}\) and \(12xy^{7}\)
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1 find the length of a, b, and c and the measure of \\( \\angle x, \\an…
### Problem 1 (i) - Parallelogram Side and Angle Calculation #### Explanation: In a parallelogram, opposite sides are equal, and opposite angles are equal. Also, consecutive angle…
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3 in the following figures (1), (2), (3), and (4) only the diagonals of…
### Question 3 (Classifying Quadrilaterals by Diagonals) #### Step 1: Recall Properties of Diagonals - **Parallelogram**: Diagonals bisect each other (no other restrictions). - **…
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dont forget! rectangles, rhombuses, and squares are all special forms o…
### Question 1 To determine the conditions to make a parallelogram a rectangle or a rhombus: - **For Rectangle (from Parallelogram):** - A parallelogram with one right angle (\(\a…
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a square with an area of ( a^{2} ) is enlarged to a square with an area…
The side length was multiplied by 5.
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graph the image of rectangle pqrs after a reflection over the line y = …
Plot the points \( P'(-9,9) \), \( Q'(-8,9) \), \( R'(-8,11) \), \( S'(-9,11) \) and connect them to get the reflected rectangle.
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graph the image of parallelogram j k l m after a reflection over the li…
Plot the points \((10,9)\), \((10,6)\), \((8,-1)\), \((8,1)\) and connect them.
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graph the image of parallelogram ( jklm ) after a reflection over the l…
Plot the points \(J'(10,9)\), \(K'(10,6)\), \(L'(8,-2)\), \(M'(8,1)\) and connect them.
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these two triangles are similar. the side with length x corresponds to …
\boxed{5.94}? Wait, no, wait, 9.90 corresponds to 5.94, so 9.90 / 5.94 = 5/3. 7.30 / 4.38 = 5/3. So 8.10 / x = 5/3 => x = 8.10 * 3/5 = 4.86. Wait, but maybe I had the corresponden…
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these figures are congruent. what series of transformations moves penta…
A. Rotation, reflection
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mrs. nash challenges ashwin and jennifer to move figure abcde onto figu…
A valid combination is: **Translate the figure 8 units left and 6 units up, then rotate \(180^\circ\) about its center** (or use reflection). Another combination: **Rotate \(180^\…
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surface area - rectangular prism decimals: s1 find the surface area of …
1) \(442.06\space ft^{2}\) 2) \(162.94\space in^{2}\) 3) \(657.12\space yd^{2}\)
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△abc is dilated by a factor of 1/3 to produce △abc. what is ac, the len…
Length of \( \overline{A'C'} \) is \( 5 \), measure of \( \angle A' \) is \( 37^\circ \).
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3 describe a sequence of rigid motions that would map △abc onto △abc
A possible sequence: 1. Translate \( \triangle ABC \) horizontally and vertically to align a vertex with the corresponding vertex of \( \triangle A'B'C' \). 2. Rotate the translat…
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5 the formula for the circumference of a circle is ( c = 2pi r ). which…
5. C. \(r=\frac{C}{2\pi}\) 6. A. \(4\)
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quadrilateral rust has a vertex at r(1,5). what are the coordinates of …
The coordinates of \(R'\) are \((6, 9)\)
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6. △mnp shown below is not drawn to scale. as shown, mn = 12 and pn = 3…
An example of a non - possible length for \(\overline{MP}\) is \(5\) (any value \(\leq9\) or \(\geq15\) would work, justification as above). ### Part (b)
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#4.) list all congruent sides or angles based on the diagrams annotatio…
\(80\)
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a 8 in thick slice is cut off the top of a cube, resulting in a rectang…
\(9.28\)
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read the passage from sugar changed the world. if you walked down beekm…
"Africans who sold other Africans as slaves insisted on being paid in fabrics from India."
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a rectangular yard measuring 36 ft by 61 ft is bordered (and surrounded…
\( 712 \) square feet (or \( 712\ \text{ft}^2 \))
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a rectangular garden measures 20 ft by 35 ft. surrounding (and borderin…
366 square feet (or \(366\ ft^2\))
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a rectangular yard measuring 36 ft by 67 ft is bordered (and surrounded…
\( 396\space ft^{2} \)
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a company makes steel rods shaped like cylinders. each rod has a radius…
$148082.4$ cubic centimeters
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a company makes wax candles in the shape of a cylinder. each candle has…
67
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a company makes wax candles in the shape of a cylinder. each candle has…
74
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at the park there is a pool shaped like a circle. a ring - shaped path …
51
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at the park there is a pool shaped like a circle with diameter 24 yd. a…
57
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a flower garden is shaped like a circle. its radius is 13 yd. a ring - …
63
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a triangle is placed in a semicircle with a radius of 7 yd, as shown be…
\( 27.93 \) square yards (or \( 27.93 \text{ yd}^2 \))
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a rectangle is placed around a semicircle as shown below. the width of …
\( 6.88 \) square centimeters
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a triangle is placed in a semicircle with a radius of 8 ft, as shown be…
\( 36.48 \) square feet (or \( 36.48\ \text{ft}^2 \))
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(a) name the sides of ∠abc. and (b) write two other names for ∠2. and (…
(a) \(BA\) and \(BC\) (b) \(\angle DBC\) and \(\angle B\) (c) \(B\)
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naming angles, sides of angles, and vertices (a) name the sides of ∠abc…
(a) \(BA\) and \(BC\) (b) \(\angle CBD\) and \(\angle B\) (c) \(B\)
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use the figure to complete each part. (a) name the sides of ∠abc. and (…
(a) \(BA\) and \(BC\) (b) \(\angle CBD\) and \(\angle B\) (c) \(B\)
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use the figure to complete each part. (a) name the vertex of \\( \\angl…
b. \(\angle2\) and \(\angle HFE\)
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graph each equation. 9) \\( \\frac { x ^ { 2 } } { 4 } + \\frac { y ^ {…
To graph \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\): 1. Recognize it is a vertical ellipse centered at \((0,0)\) with \(a = 3\) (semi - major axis) and \(b=2\) (semi - minor axis). 2. …
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worksheet 19 date: the map of a vegetable garden is given below, where …
- Carrots perimeter: \(16\)m - Beans perimeter: \(14\)m - Cabbages perimeter: \(14\)m - Potatoes perimeter: \(18\)m - Entire garden perimeter: \(34\)m
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find the value of x. x = □
\(x = 61\)
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determine whether a triangle with the given vertices is a scalene, isos…
(a) Isosceles triangle (check "Isosceles triangle" for (a)) (b) Scalene triangle (check "Scalene triangle" for (b)) (c) Scalene triangle (check "Scalene triangle" for (c))
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triangle c
Scalene (debe marcarse el cuadro junto a "Scalene")
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triangle b scalene isosceles equilateral
Equilateral (la opción a seleccionar es la casilla junto a "Equilateral")
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toys the face of a toy block can be modeled by a triangle. solve for x …
\(x = 12\), \(y = 3\)
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question 5 5.6 class practice solve for x. solve for y.
For \( x \): \( \boldsymbol{4} \) For \( y \): \( \boldsymbol{18.5} \)
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question 4 5.6 class practict solve for x. 22 solve for y.
For \( x \): \( 22 \) For \( y \): \( 5 \)
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billiards a billiards ball rack can be modeled by △abc. solve for x.
\(x = 22\)
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find the value of x.
\( x = 5 \)
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find the value of x.
\(22\)
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(a) linear pair: ∠ and ∠ (b) vertical angles: ∠ and ∠ (c) supplementary…
(a) Linear pair: \(\angle1\) and \(\angle2\) (answers may vary depending on the pair chosen from the figure, another valid pair could be \(\angle5\) and \(\angle6\) etc.) (b) Vert…
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for the figure below, give the following. (a) one pair of angles that f…
(a) \(\angle1\) and \(\angle2\) (b) \(\angle5\) and \(\angle7\) (c) \(\angle6\) and \(\angle7\)
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for the figure below, give the following. (a) one pair of angles that f…
(a) Linear pair: $\angle1$ and $\angle2$ (b) Vertical angles: $\angle5$ and $\angle7$ (c) Supplementary angles: $\angle6$ and $\angle7$
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(a) an angle measures 138°. what is the measure of its supplement? (b) …
measure of the supplement: \(42\) measure of the complement: \(65\)
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(a) an angle measures 70°. what is the measure of its supplement? (b) a…
measure of the supplement: \(110\) measure of the complement: \(41\)
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(a) an angle measures 60°. what is the measure of its complement? (b) a…
measure of the complement: \(30^{\circ}\) measure of the supplement: \(112^{\circ}\)
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for each graph, decide if the two lines are parallel, perpendicular, or…
Graph 1: Neither Graph 2: Parallel Graph 3: Neither Graph 4: Parallel
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try again one of your answers is incorrect. for each graph, decide if t…
Graph 1: Parallel Graph 2: Perpendicular Graph 3: Perpendicular Graph 4: Neither
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one of your answers is incorrect. for each graph, decide if the two lin…
Graph 1: Parallel Graph 2: Perpendicular Graph 3: Neither Graph 4: Neither
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for each graph, decide if the two lines are parallel, perpendicular, or…
Graph 1: Parallel Graph 2: Perpendicular Graph 3: Neither Graph 4: Neither
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for each graph, decide if the two lines are parallel, perpendicular, or…
Graph 1: Neither Graph 2: Perpendicular Graph 3: Parallel Graph 4: Perpendicular
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use the figure to complete each part. (a) write two other names for ∠qm…
(a) $\angle PMQ$ and $\angle 2$ (b) $M$ (c) $MQ$ and $MN$
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question 5 (multiple choice worth 2 points) (06 01 mc) the cross sectio…
Volume A = Volume B
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question 4 (multiple choice worth 2 points) (06.01 mc) a circle has bee…
27.52 units² (corresponding to the option with 27.52 units²)
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use the figure to complete each part. (a) write two other names for \\(…
(a) \(\angle PMQ\) and \(\angle2 + \angle1\) (b) \(M\) (c) \(MQ\) and \(MN\)
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question 2 (fill - the - blank worth 2 points) (05.01 mc) the stack on …
\( 360 \)
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building design the aldar properties headquarters building in the unite…
Para completar la prueba: - \( \overline{AB} \) es congruente a \( \overline{DC} \) (dado, ya que se indica \( AB \cong DC \)). - \( \overline{BD} \) es congruente a \( \overline{…
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question 1 (multiple choice worth 2 points) (05.01 mc) a rectangular pr…
The correct option is the one with the description: "A rectangular prism in which \( BA = 30 \) and \( h = 5 \) has a volume of 150 units³, therefore, Shannon is correct" (assumin…
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(a) name the sides of \\( \\angle gfe \\). and (b) write two other name…
(a) \(FG\) and \(FE\) (b) \(\angle EFH\) and \(\angle HFE\) (c) \(F\)
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building design the aldar properties headquarters building in the unite…
To solve the proof that \( \triangle ABD \cong \triangle DCA \), we analyze the given information and congruence properties: ### Step 1: Identify Congruent Sides (First Blank) We …
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naming angles, sides of angles, and vertices (a) name the sides of ( an…
(a) \( \overrightarrow{FG} \) and \( \overrightarrow{FE} \) (b) \( \angle EFH \) and \( \angle HFE \) (c) \( F \)
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complete the following proof. given: (overline{ac}perpoverline{db}) and…
1. \( \angle DCA \) and \( \angle BCA \) are **right** angles because \( \overline{AC} \) and \( \overline{DB} \) are **perpendicular**. 2. By the **reflexive property of congruen…
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classify each figure as a line, ray, or line segment. then, show how to…
| Figure | Type | How to write it | | --- | --- | --- | | (a) | line segment | \(\overline{GH}\) | | (b) | line | \(\overleftrightarrow{LM}\) | | (c) | ray | \(\overrightarrow{KJ}…
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given : qr ≅ rs and ∠qrt ≅ ∠srt prove : △qrt ≅ △srt qr ≅ rs given rt ≅ …
\(\triangle QRT\cong\triangle SRT\) by the SAS (Side - Angle - Side) congruence criterion.
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classify each figure as a line, ray, or line segment. then, show how to…
(a) Type: line, How to write it: $\overleftrightarrow{DC}$ (or $\overleftrightarrow{CD}$) (b) Type: line segment, How to write it: \(\overline{FE}\) (or \(\overline{EF}\)) (c) Typ…
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given: \\( \\overline{ab} \\cong \\overline{dc}, \\overline{ab} \\paral…
\(\triangle ABC\cong\triangle DCB\) by the SAS (Side - Angle - Side) congruence criterion.
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classify each figure as a line, ray, or line segment. then, show how to…
| Figure | Type | How to write it | |--|--|--| | (a) | ray | \(\overrightarrow{HG}\) | | (b) | line | \(\overleftrightarrow{KJ}\) (or \(\overleftrightarrow{JK}\)) | | (c) | line s…
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classify each figure as a line, ray, or line segment. then, show how to…
(a) ray, $\overrightarrow{SR}$; (b) line segment, $\overline{PQ}$; (c) line, $\overleftrightarrow{TU}$
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part c — stem challenge question you are designing a package that uses …
Sphere. Because for a given volume, the sphere has the minimum surface - area among cylinder, rectangular prism and sphere.
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5. application problem a company wants to design a container that holds…
a. The height of the cylinder is approximately \(12.3\space cm\). b. The height of the rectangular prism is approximately \(14.6\space cm\). c. The cylinder requires less surface …
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5. application problem a company wants to design a container that holds…
a. The height of the cylinder is approximately \(12.4\space cm\) b. The height of the rectangular prism is approximately \(14.6\space cm\) c. The cylinder requires less surface ar…
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4. sphere a spherical sports ball has a radius of 7 cm. a. find the sur…
a. The surface area is approximately \(615.44\mathrm{cm}^{2}\). b. The volume is approximately \(1436.03\mathrm{cm}^{3}\).
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3. cone a cone has a radius of 3 cm and height 12 cm. a. find its slant…
a. The slant height is \(3\sqrt{17}\text{ cm}\approx12.37\text{ cm}\). b. The surface area is \(9\pi(1 + \sqrt{17})\text{ cm}^{2}\approx144.7\text{ cm}^{2}\). c. The volume is \(3…
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2. rectangular prism a gift box measures ( 10 mathrm{~cm} \times 8 math…
a. The total surface area is \(376\space cm^{2}\). b. The volume is \(480\space cm^{3}\).
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mbc = \\frac{e - 0}{1 - 0} = \\frac{e}{1} = e application of the slope …
D. \((d - e)^{2}\)
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part b — calculation problems 1. cylinder a cylindrical water bottle ha…
a. The surface area is approximately \(477.28\) \(cm^{2}\). b. The volume is approximately \(753.6\) \(cm^{3}\).
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part a — formula recall (fill in the blanks) 1. surface area of a cylin…
1. $2\pi r^{2}+2\pi rh$ 2. $\frac{1}{3}\pi r^{2}h$ 3. $2lw + 2lh + 2wh$ 4. $\frac{4}{3}\pi r^{3}$ 5. $B+LSA$
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in triangle def, dg = 10 cm. what is cg? 5 cm 10 cm 15 cm 20 cm
A. 5 cm
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in which type of triangle is the orthocenter on the perimeter of the tr…
a right triangle
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in which figure is point g an orthocenter?
The figure with triangle \( \triangle ACB \) (the first triangle with right angle at \( C \)) has point \( G \) as the orthocenter. (Assuming the first option's triangle is the on…
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in triangle def, cg = (x + 5) units and dg = (3x - 2) units. what is dg…
34 units
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in triangle nlm, point s is the centroid, qs = (3x - 5) cm, and ns = (4…
20 cm
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if an orthocenter lies inside of a triangle, then the triangle must be …
D. acute.
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in triangle abc, eg = x inches and bg = (5x - 12) inches. what is eb? 2…
12 inches
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point g is the centroid of triangle abc. ag = (5x + 4) units and gf = (…
51 units
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a centroid is the intersection of three altitudes in a triangle. perpen…
D. medians in a triangle.
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in triangle nql, point s is the centroid, ns = (x + 10) feet, and sr = …
7 feet
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read the proof that shows that the medians of an isosceles triangle mee…
First blank: midpoint Second blank: vertex Third blank: medians
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g is the centroid of triangle abc. what is the length of \\overline{ae}…
36