Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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select the correct answer. in the diagram, point m is the center of the…
B. \( 67^\circ \)
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follow these steps to derive the law of cosines. 1. the relationship be…
Pythagorean theorem
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what must be the value of x so that lines c and d are parallel lines cu…
18
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# 3-5 draw and label each angle 3. ∠tan 4. ∠big 5. ∠sml
- For \( \angle TAN \): Drawn with vertex \( A \), rays \( AT \) and \( AN \), and labeled \( \angle TAN \). - For \( \angle BIG \): Drawn with vertex \( I \), rays \( IB \) and \…
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all the edges of the object in the diagram are equal in length. the obj…
C. a rhombus
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graph a right triangle with the two points forming the hypotenuse. usin…
Leg 1: 2, Leg 2: 2, Hypotenuse: \(2\sqrt{2}\)
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the given line segment has a midpoint at (-1, -2). what is the equation…
\(y = -4x - 6\) (corresponding to the option \(y = -4x - 6\))
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a1. career exploration and planning the first and most important step i…
This is a worksheet for career exploration and planning. Since no specific question (like choosing an inventory, listing careers, or a specific inquiry about the task) is provided…
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geometry chapter 1 homework 1.3 #1-2 name each angle in three different…
\( \angle E \), \( \angle IEN \), \( \angle NEI \)
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3 you can also change the scale on a scale drawing to make the represen…
A scale drawing of a door with a scale of \(1\) in. : \(6\) ft would be shorter than a scale drawing of the same door with a scale of \(1\) in. : \(3\) ft. This is because in the …
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unit 1 test study guide (geometry basics) name: amin shaath date: _____…
\( M \) and \( N \) (or other valid collinear points like \( J \) and \( L \) if misinterpreted, but likely \( M \) and \( N \)) ### Question 2: Give another name for line \( b \)
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question 5 is ∠def the same as ∠fed ? yes no depends on the angle measu…
Yes (corresponding to the option "Yes")
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9. triangle abc has vertices a (-4, -2), b (-1, 3), and c (5, 0) what c…
The clockwise angle of rotation about the origin is \( 90^\circ \) (or \( \frac{\pi}{2} \) radians, but in degrees, it's \( 90^\circ \)).
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name the indicated angle options: ∠hij, ∠mhj, ∠jmh, ∠hmg
$\angle JMH$
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example heather uses centimeter grid paper to draw a scale diagram of h…
The dimensions are not the same. With \(1\space\text{cm}:16\space\text{m}\), the drawing dimensions are \(2\space\text{cm}\times3\space\text{cm}\); with \(1\space\text{cm}:8\space…
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name the indicated angle options: ○ ∠kim ○ ∠iml ○ ∠ikl ○ ∠kmi
\(\boldsymbol{\angle KMI}\)
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name the indicated angle. options: ∠gmj, ∠jml, ∠gml, ∠gmk
\( \angle GMJ \)
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∠1 and ∠2 are supplementary angles. if m∠1 = (4x - 9)° and m∠2 = (5x + …
103
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9. triangle abc has vertices a (-4, -2), b (-1, 3), and c (5, 0). what …
90°
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name the indicated angle. options: ∠hmi, ∠mlh, ∠gmh, ∠hml
\(\boldsymbol{\angle HML}\)
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∠1 and ∠2 are vertical angles. if ( mangle 1 = (x + 11)^circ ) and ( ma…
-2
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1 cool-down s t b h b 1. what are the values of b and h for each parall…
Parallelogram S: \( b = 6 \) units, \( h = 5 \) units Parallelogram T: \( b = 4 \) units, \( h = 6 \) units (Note: The exact values depend on the grid size, but assuming each grid…
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arty says that if you change a scale so that a unit represents a longer…
I do not agree with Arty's statement. For example, let the original scale be \( 1 \text{ cm} : 1 \text{ m} \) (1 cm on the drawing represents 1 m in reality) and the new scale be …
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if angle three is equal to 6x+16 and angle seven is equal to 2x+2, solv…
-3.5
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1. enter your answer. what is the side length of a square that has an a…
The side length of the square is 9 units. This is because the area of a square is calculated by squaring the side length (\( A = s^2 \)). Given the area is 81 square units, we sol…
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in δabc, d and e are midpoints of ab and ac, respectively. prove that d…
a. Midsegment Theorem ### Second Question (Properties of Similar Triangles)
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if line m || line n and ∠2 measures 47°, what is the measure of ∠5? dia…
\( 133^\circ \) (corresponding to the option "133°")
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find the value of c and yz if y is between x and z. xy = 11, yz = 4c, x…
\( c = 18 \); \( YZ = 72 \)
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prove that △abd ≅ △acd in isosceles △abc, where ab = ac and ad is the a…
c. SAS Congruence ### Second Question (Midsegment of a Triangle)
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prove that △xyz ~ △pqr using aa similarity, where ∠x = ∠p and ∠z = ∠r. …
c. \(\angle Z=\angle R\) ### Second Sub - Question (Triangle Transformation)
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raul’s hamster’s house sits in the corner of its cage as shown in the d…
\(15x + 65\)
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cool-down r-graueuegrams s ana t are each labeled with a base and a cor…
Parallelogram \( S \): \( b = \boldsymbol{6} \) units, \( h = \boldsymbol{5} \) units. (Note: The exact values depend on the grid scale, but typical grid problems use integer coun…
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what must be true for two triangles to be congruent? a. only the angles…
b. All corresponding sides and angles must be equal ### Second Question (Prove that $\boldsymbol{\triangle PQR \cong \triangle XYZ}$ using ASA congruence...):
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the diagram shows a border that is 4 inches wide surrounding annie’s pa…
\( 24x + 160 \)
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shade in a rectangle with an area of 42 square units.
To shade a rectangle with an area of 42 square units, we can use the formula for the area of a rectangle, \( A = l \times w \) (where \( l \) is length and \( w \) is width). We n…
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incorrect 2 tries left. please try again. find the measure of (overline…
26
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15. higher order thinking the length of a rectangle is twice the width.…
### Part a # Explanation: ## Step1: Define variables Let the width of the rectangle be \( w \). Then the length is \( 2w \) (since length is twice the width). ## Step2: Use area f…
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find the value of a and yz if y is between x and z. xy = 3a − 4, yz = 6…
\( a = 6 \); \( YZ = 38 \)
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3. find the area of rectangle jklm round to the nearest tenth if necess…
101.6
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∠1 and ∠2 are complementary angles. if ( mangle 1 = (3x + 7)^circ ) and…
$85^\circ$
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jermaine draws a scale drawing of a porch on a grid with 1 - centimeter…
The actual area of the porch is \(864\) square feet.
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in the figure, line e || line f. which statement is true? options: ○ ( …
# Explanation: ## Step1: Analyze ∠6 ∠6 and the 110° angle are vertical angles? No, wait, ∠6 and the 110° angle: actually, ∠5 and 110° are supplementary? Wait, no, ∠5 and 110° are …
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question solve for the value of ( k ). (3k+8)° 112°
20
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practice - area on the coordinate plane 1. find the area of parallelogr…
21
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solve. 5 diagrams a and b are scale drawings of the same field. each sq…
\( 1 \) cm : \( 96 \) ft #### Problem 6: Area of actual field
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solve for the value of k.
13
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in the figure, line ( e parallel ) line ( f ). which statement is true?…
# Explanation: ## Step1: Analyze ∠6 and 110° angle ∠6 and the 110° angle are vertical angles? No, wait, the 110° angle and ∠5 are supplementary? Wait, no, the 110° angle and ∠5: a…
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which of the angles in the figure are supplementary to angle 4? figure:…
\(\boldsymbol{\angle 2,\angle 3,\angle 6}\) and \(\boldsymbol{\angle 7}\) (the first option)
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in the figure, the angles are formed by a transversal and two parallel …
D1 @ D3 @ D5 @ D7; D2 @ D4 @ D6 @ D8
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graph the points (7, −1), (3, 5), and (−8, −4) on the coordinate plane.…
The points \((7, -1)\), \((3,5)\), and \((-8, -4)\) are graphed on the coordinate plane by following the steps of moving along the x - axis and y - axis as described.
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1. triangles are considered similar if their corresponding angles are _…
congruent (or equal) ### Question 2:
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which angle is not congruent to $\\angle 4$? diagram: two parallel line…
$\boldsymbol{\angle 7}$
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if line m || line n and ∠2 measures 35°, what is the measure of ∠5? dia…
\( 145^\circ \) (corresponding to the option "145°")
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solve for the value of t.
7
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$\\sqrt{(3 - 2)^2 + (10 - 7)^2}$
\(\sqrt{10}\) (or approximately \(3.16\))
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find the measure of the missing angles. answer attempt 1 out of 2 g = s…
\( g = 118^\circ \), \( h = 62^\circ \), \( k = 133^\circ \), \( m = 47^\circ \)
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which of the angles in the figure are supplementary to ∠3? figure with …
\(\angle1,\angle4,\angle5\) and \(\angle8\) (the option with \(\angle1,\angle4,\angle5\) and \(\angle8\))
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find cd b •———• c —————• d 2 2x - 6 blue arrow from b to d labeled x + …
14
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find the distance between the two points rounding to the nearest tenth …
\( 10.8 \)
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find the measure of the missing angle. answer attempt 1 out of 2 a = su…
$35^\circ$
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if angle four is equal to 4x - 6 , and angle 6 is equal to 2x-12 , solv…
33
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lets try: right triangle pqr has an area of 25 units. determine which o…
# Explanation: First, we need to identify the coordinates of points \( P \) and \( Q \) from the graph. From the graph, point \( P \) is at \( (-5, 1) \) and point \( Q \) is at \…
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solve the problems. 1 sara uses a scale of 1 cm : 12 m to draw a floor …
### Part 1: Determine if the scale makes the drawing larger To make the drawing larger, the new scale should represent more meters per centimeter than the original scale (\(1\) cm…
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find the distance between the two points rounding to the nearest tenth …
\( 11.3 \)
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point s is between r and t on rt. find the length of rs if: rs = 2x + 1…
20
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find the distance between the two points rounding to the nearest tenth …
\( 6.4 \)
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find the measure of the missing angles. answer attempt 1 out of 2 d = \…
\( d = 56^\circ \), \( e = 27^\circ \), \( f = 56^\circ \)
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select the correct answer from the drop-down menu. a cylinder is sliced…
an ellipse
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find df d •——• e ——• f de: ( x + 7 ), ef: ( 7 ), df: ( 4x + 2 ) ( df = …
18
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lets try: find the area of parallelogram klmn round to the nearest tent…
36
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what must be true for the sas criterion to apply? ○ a. two angles must …
d. Two pairs of corresponding sides must be proportional, and the included angle must be congruent ### Second Question (Similar Triangles - SSS Criterion)
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find the distance between the two points rounding to the nearest tenth …
\( 7.6 \)
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6 a science museum has a scale model of a beetle. the scale factor is 5…
50000
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select the correct answer. a prism whose base is a 9-sided polygon is i…
D. when the plane makes a narrow angle with the base
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points a, b, and c are collinear. point b is between a and c. find ab i…
13
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reviewing the cosine ratio which cosine ratios are correct for △pqr? ch…
# Explanation: ## Step1: Recall cosine definition In a right triangle, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\triangle PQR$ (right-angled at $Q$): - For $…
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a surveyor measures two triangular plots of land. in the first plot, th…
c. Yes, by the SAS Criterion ### Second Question:
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find the distance between the two points rounding to the nearest tenth …
15.0
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select the correct answer. what is the shape of the cross section indic…
D. circle
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lets try: find the area of δabc. round to the nearest tenth if necessar…
31.5
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find the distance between the two points rounding to the nearest tenth …
10
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solve for x. 2x - 4 2x - 7 t •——•——• v u 17 x = 12
\( x = 7 \)
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select a point that has the minimum x-value. (●) enter the minimum x-va…
The equation or inequality for the domain is \(\boldsymbol{-16\leq x\leq20}\)
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a building casts a shadow 20 meters long, and a 4 - meter pole casts a …
a. 20 meters ### Second Question (Similar Triangles \( \triangle ABC\sim\triangle DEF \))
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2 select the correct answer from each drop-down menu. a circle is rotat…
The three - dimensional shape resulting from the rotation is a ring with a hollow center. So the second drop - down answer is hollow.
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points a, b, and c are collinear. point b is between a and c. solve for…
\( -1 \)
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2 select the correct answer from each drop-down menu. a circle is rotat…
First drop - down: ring (Note: Since the second drop - down options are not fully visible, but based on the first part, the first answer is "ring". If more details about the secon…
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5 petra wants to represent a distance of 400 miles on a piece of notebo…
No, Petra cannot make this scale drawing. Because with a scale of \(1\) in. \( = 20\) mi, a \(400\)-mile distance would require a drawing length of \(\frac{400}{20}=20\) inches, b…
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solve for x. 22 + 2x 8 r • q • p x + 20 x= 10
\( x = -10 \)
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select the correct answer. a triangular pyramid is cut by a plane. in w…
D. when the plane intersects the base and all three lateral faces of the pyramid
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13. a ladder leans against a wall, forming a 90° angle with the ground.…
d. AA (Angle - Angle) ### Question 14
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lets try: find the area of rectangle efgh. round to the nearest tenth i…
The area of rectangle EFGH is \(\boxed{30}\) (or 30.0 when rounded to nearest tenth).
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points a, b, and c are collinear. point b is between a and c. solve for…
\( x = 7 \) ### Problem 9 (Top - Right)
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10. what happens to the corresponding sides of two similar triangles? a…
c. They are proportional to each other. ### Question 11
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lets try: find the area of rectangle efgh. round to the nearest tenth i…
The area of rectangle EFGH is approximately 30.2.
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7. a triangle with side lengths 5, 12, and 13 is dilated to create a si…
a. 6 ### Question 8
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directions: find the value of x based on the information given for each…
s: 12. \( x = \boldsymbol{4} \) 14. Volume = \( \boldsymbol{210 \, \text{cm}^3} \), Surface Area = \( \boldsymbol{214 \, \text{cm}^2} \) (assuming rectangular prism) 15. \( \angle…
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4. in $\\triangle abc$, the angle bisector of $\\angle bac$ intersects …
c. $\boldsymbol{\frac{BD}{DC}=\frac{AB}{AC}}$ ### Question 5
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1. which of the following statements is *not* true about similar figure…
b. Similar figures must be the same size ### Question 2
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6. abcdef is a regular hexagon with vertex a(-7, 0) and b(-3, 3). tyron…
Tyrone is correct because the length of side \( AB \) is 5 units (calculated via the distance formula), and a regular hexagon with 6 equal sides of length 5 has a perimeter of \( …