几何
三角形、圆、解析几何与证明题。
-
determine which of these are right triangles. sort the cards into two p…
Right Triangle Not a Right Triangle Right Triangle Not a Right Triangle Not a Right Triangle Not a Right Triangle Right Triangle Not a Right Triangle
-
in the diagram below of triangle mno, p is the midpoint of \\(\\overlin…
The measure of \( \overline{MN} \) is \( 48 \).
-
in the diagram below of triangle bcd, e is the midpoint of \\(\\overlin…
\( 108 \)
-
topic: degree and radian measure progress: the movement of the progress…
B. $-120^\circ$
-
texascollegebridge study paths tx math bridge - stage 2 topic test: deg…
$\frac{5\pi}{3}$
-
in the diagram below of triangle cde, f is the midpoint of \\(\\overlin…
\( 40 \)
-
draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is \(-3\)
-
sa \\o= 4\\pi r^2 \\quad sa\\blacktriangle\\ = \\pi r^2 + \\pi rs v \\t…
(for Problem 1): SA = \( \boldsymbol{4747.68 \, \text{mm}^2} \) V = \( \boldsymbol{24617.6 \, \text{mm}^3} \) (For Problem 2, SA ≈ \( 300.26 \, \text{yd}^2 \), V ≈ \( 299.44 \, \t…
-
sort the words according to the meanings of their shared roots. straigh…
- Under "straight": rectangle, direct - Under "no or not": neglect, negate, negation, negative
-
students sometimes mix these up - so here they are together: if $(a + b…
Yes Because \(3^{2}+4^{2}=9 + 16=25=5^{2}\), so by the Pythagorean theorem, it is a right - triangle.
-
the measures of the angles of a triangle are shown in the figure below.…
The measure of the smallest angle is \(\boxed{\frac{271}{7}}\) (or approximately \(38.71^\circ\)). Wait, but maybe the problem expects an integer. Wait, maybe I misread the angles…
-
how could brent use a rectangle to model the factors of $x^2 - 7x + 6$?…
C. He could draw a diagram of a rectangle with dimensions \(x - 1\) and \(x - 6\) and then show the area is equivalent to the sum of \(x^2\), \(-x\), \(-6x\), and \(6\).
-
the expression $40x^2 - 65x + 50$ represents the sum of the interior an…
B. $2(8x^{2}-13x + 10)$
-
zohar is using scissors to cut a rectangle with a length of 5x - 2 and …
C. \( 2(5x - 2)+2(3x + 1) \); 62 centimeters (assuming the third option is labeled C, if not, the option with \( 2(5x - 2)+2(3x + 1) \) and 62 centimeters)
-
ok, heres another one (you can always go back a slide if you need to se…
13.3
-
read the first part of the story. the glass studio \what do you think, …
Gabriella has most likely been to so many stores because she and her dad are searching for a send - off gift for her sister Carmen, who is leaving for art school next week, and th…
-
solve for x. the polygons in each pair are sin 24) 10 15 x+4 21 10 15 w…
\(x = 10\) ### Problem 25: Transformation Rule
-
a side of the triangle below has been extended to form an exterior angl…
\(x = 21\)
-
choose the best graph that represents the linear equation: x = -3 graph…
The graph that represents \( x = -3 \) should be a vertical line passing through \( x = -3 \) on the x - axis. Looking at Graph A, we need to check the x - coordinate of the verti…
-
in $\\triangle jkl$, $\\overline{jl}$ is extended through point $l$ to …
$58$
-
in δuvw, m∠u = (x − 6)°, m∠v = (5x + 6)°, and m∠w = (3x + 18)°. what is…
\(x = 18\)
-
question determine the type of triangle that is drawn below. (image of …
Isosceles Acute
-
find the equation of a line parallel to $-3x + y = -9$ that passes thro…
\(y = 3x - 14\) (the fourth option: \(y = 3x - 14\))
-
find the equation of a line parallel to $y + 9 = x$ that passes through…
D. \( y - 5 = x - 4 \) (assuming the last option is D, with the option text \( y - 5 = x - 4 \))
-
lt2.3 i can find the area of compound figures. 3. show how you can divi…
The area of the shaded region is \( 135 - 25\pi\approx56.5 \) square yards (or \( 135 - 78.5 = 56.5 \) square yards if \( \pi\approx3.14 \)).
-
find the slope of the line that passes through (7, 6) and (10, 5). simp…
\(-\frac{1}{3}\)
-
select the correct answer. consider the formula for the slope between t…
B. \( y_2 = m(x_2 - x_1) + y_1 \)
-
given, ab ≅ de, bc ≅ ef, prove: ac ≅ df (there are line segments: ac wi…
\( AC = DF \) (proven using Segment Addition Postulate and Transitive Property with given \( AB = DE \) and \( BC = EF \))
-
find the area. the figure is not drawn to scale. image of a composite f…
144.5 cm²
-
4. complete the proof below by giving the missing statements and reason…
By using the segment addition postulate and the properties of equality (substitution and subtraction), we have proven that \( AB = EF \). The final answer is that \( AB \) is equa…
-
1. complete the proof below by choosing the missing statements and just…
\( AB = EF \) (by using segment addition postulate, substitution with given equalities, and subtraction property of equality)
-
what is the area of the kite? (image of a kite with diagonals: one diag…
72 n²
-
you are planning to use a ceramic tile design in your new bathroom. the…
D. 55.4 cm²
-
triangle efg with sides ef=10, eg=15, fg=27.5 (and another figure with …
If scale factor (from \( EFG \) to \( E'F'G' \)): \( \frac{2}{5} \) (or 0.4). If finding \( E'G' \) (corresponding to \( EG = 15 \)): 6. If finding \( F'G' \) (corresponding to \(…
-
find the area of the regular polygon. round your answer to the nearest …
483.0 m² (Note: The options have unit "in²" which may be a typo; the calculation uses given metric units)
-
there are two triangles (or similar figures) with labeled sides: left f…
The missing side length is 6 (assuming the triangles are similar and using the proportion of corresponding sides).
-
the figures are similar. give the ratio of the perimeters and the ratio…
The ratio of perimeters is $\frac{9}{8}$ and the ratio of areas is $\frac{81}{64}$ (the last option in the image, assuming it's labeled correctly as the option with $\frac{9}{8}$ …
-
question 7 1 pts the triangles are similar. the area of the larger tria…
431 ft²
-
what number can you multiply each length in the scale drawing by to fin…
The number is \(3\) (where multiplying the scale - drawing length (in inches) by \(3\) gives the actual length in feet).
-
the diagram shows two parallel lines cut by a transversal. one angle is…
45
-
20) a) similar; sss and sas similarity b) not similar c) similar; aa si…
D. similar; SAS similarity ### Problem 21
-
select the correct answer. to which category of drugs does cocaine belo…
A. stimulants
-
question express the interval using two different representations. (-3,…
Inequality Notation: \(-3 < x < -1\) Number Line: Open circles at \(-3\) and \(-1\) with a line segment between them.
-
for each number below, is it even or odd? 510 \todd \teven 28 \todd \te…
- 510: Even (select the circle under "Even") - 28: Even (select the circle under "Even") - 72: Even (select the circle under "Even") - 91: Odd (select the circle under "Odd") - 29…
-
point t is on line segment \\( \\overline{su} \\). given \\( su = 5x \\…
6
-
use pythagorean theorem to answer the following question. andrew walks …
1.25
-
given that the ( v = 450 , \text{m}^3 ) and the ( h = 15.2 , \text{m} )…
B. 3.1 m
-
question express the interval using two different representations. 3,9 …
Inequality Notation: \(3 \leq x \leq 9\) Number Line: Closed circles at 3 and 9 on the number line (from -12 to 12) with a line segment connecting them.
-
qt || rs and qt ≅ rs. complete the proof that δqtu ≅ δsru. image of tri…
1. Reason: Given 2. Reason: Given 3. Reason: Vertical Angles Theorem 4. Reason: Alternate Interior Angles Theorem 5. Reason: ASA (Angle - Side - Angle) Congruence Criterion
-
jill wants to place a small fence around her garden. an outline of the …
C. 24 ft.
-
complete the proof that ( mangle q + mangle u + mangle qru = 180^circ )…
1. Given 2. Corresponding Angles Postulate 3. Alternate Interior Angles Theorem 4. Angle Addition Postulate 5. Substitution Property of Equality 6. Linear Pair Postulate (suppleme…
-
4. complete the proof by dragging the missing statements and justificat…
The completed proof uses the given congruent angles, angle addition postulate, substitution property, transitive property, and definition of congruence to show $\angle RSV \cong \…
-
question 11 triangle abc and triangle def are shown on the coordinate p…
\( \triangle ABC \cong \triangle FED \) by SAS (the option with " \( \triangle ABC \cong \triangle FED \) by SAS ")
-
express the interval using two different representations. $x < -7$ or $…
Interval Notation: \( (-\infty, -7) \cup (-4, \infty) \) Number Line: Open circle at -7 with left arrow, open circle at -4 with right arrow.
-
given that the r = 6 m and the h = 7 m, find the surface area of the cy…
The surface area of the cylinder is \( 489.84 \) square meters.
-
$\\overline{hi} \\parallel \\overline{gj}$ and $\\overline{gh} \\parall…
1. Reason: Given 2. Reason: Given 3. Reason: Alternate Interior Angles Theorem 4. Reason: Alternate Interior Angles Theorem 5. Reason: Reflexive Property of Congruence 6. Reason: …
-
4. complete the proof below by proving the missing statements and justi…
To prove $\angle RSV \cong \angle UST$ given $\angle RSU \cong \angle VST$: 1. **Statement**: $\angle RSV = \angle RSU + \angle USV$, $\angle UST = \angle VST + \angle USV$ **Just…
-
larry has a garden that is in the shape of a rectangle with a length of…
C. 10 bags
-
wy ⊥ xy. complete the proof that m∠w + m∠x = 90°. (image of triangle xy…
For Statement 2, Reason: Definition of perpendicular lines (if two lines are perpendicular, they form a \( 90^\circ \) angle). For Statement 3, Reason: Triangle Angle Sum Theorem …
-
find the missing length. the triangles in each pair are similar. 22) $\…
The missing length (AC) is 60.
-
the diagram shows two parallel lines cut by a transversal. one angle me…
To determine the measure of angle \( C \): 1. First, identify the angle vertical to the given \( 38^\circ \) angle. Vertical angles are equal, so this vertical angle is also \( 38…
-
21. draw and find the equation of one of the diagonal lines of symmetry…
One possible equation is \(y = x\) (or \(y = -x\), or \(y = 0\), but the most probable for a square's diagonal line of symmetry in function form is \(y = x\) or \(y = -x\); here, …
-
given the circle below, if be = 24 and dg = 6, what is cg? options: 4, …
18
-
4. complete the proof below by proving the missing statements and reaso…
To solve this angle - proof problem, we follow these steps: ### Step 1: Identify the given information We are given that \(\angle RSV\cong\angle VST\). By the definition of congru…
-
the diagram shows two parallel lines cut by a transversal. one angle is…
37
-
use pythagorean theorem to answer the following question. rodney walks …
26.9
-
complete the proof that ( mangle rqt = mangle p + mangle t ) without us…
- Statement 2 Reason: Corresponding Angles Postulate - Statement 3 Reason: Alternate Interior Angles Theorem - Statement 5 Reason: Substitution Property
-
8. reflect the triangle across the diagonal line $y = x$ and draw the i…
To solve, follow these steps: 1. **Find Coordinates**: Determine \((x, y)\) for \( M \), \( N \), \( O \) from the grid. 2. **Reflect Over \( y = x \)**: Swap \( x \) and \( y \) …
-
complete the proof that ( mangle v + mangle z + mangle vwz = 180^circ )…
Substitution (or Substitution Property of Equality)
-
7. rotate the triangle 90° counterclockwise about the origin and draw t…
The rotated triangle has vertices \( P'(0, 1) \), \( Q'(0, 3) \), \( S'(-3, 0) \) (plot these points and draw the triangle).
-
each circle counts as one whole. write a mixed number giving the amount…
(a) Mixed number: \(1\frac{1}{4}\) (b) Improper fraction: \(\frac{5}{4}\)
-
(problems 5-8 are worth 3 pts each. 1 for each labe 5. reflect the tria…
The reflected triangle has vertices \( A'(4, -1) \), \( B'(-2, 0) \), \( C'(1, 3) \) (plotted and connected on the grid as the image).
-
calculate the area of this trapezoid: a 28 units², b 32 units², c 40 un…
A. 28 units²
-
complete the proof that $m\\angle g + m\\angle f = 90^\\circ$. | statem…
Subtraction Property of Equality (or Subtract \( 90^\circ \) from both sides of the equation)
-
if ( l = 4 , \text{cm} ), ( w = 3 , \text{cm} ), and ( h = 12 , \text{c…
D. \( 144 \, \text{cm}^3 \)
-
given this rectangular prism with length = 1.2 m, height = 1.3 m, and v…
The missing width of the rectangular prism is \( 2.1 \, \text{m} \).
-
16. in \\( \\triangle jkl \\), if \\( m\\angle k \\) is nine more than …
\( m\angle J = 75^\circ \), \( m\angle K = 57^\circ \), \( m\angle L = 48^\circ \)
-
given this square pyramid with height = 50 m and volume = 15,000 m³, fi…
\( 30 \)
-
if l = 5 m, w = 8 m, and h = 4 m, calculate the volume of the prism:
The volume of the prism is \( 160 \, \text{m}^3 \).
-
18) $\\triangle fgh \\sim \\triangle abc$ 19) $\\triangle uvw \\sim \\t…
D) not similar ### Problem 19:
-
if ( l = 13.1 ) ft., ( w = 45.5 ) ft., and ( h = 33.6 ) ft., calculate …
\( 20027 \, \text{ft}^3 \) (corresponding to option D: 20,027 ft.³)
-
14. in \\( \\triangle rst \\), if \\( m\\angle r \\) is five more than …
\( x = 19 \), \( m\angle R = 43^\circ \), \( m\angle S = 20^\circ \), \( m\angle T = 117^\circ \) ### Problem 15:
-
barry is a city worker and is in charge of putting sand on the playgrou…
D. 112 bags of sand
-
a mall is redesigning a section of the food court that will expand the …
75.7
-
12. find the values of x and y in the diagram below. (4y - 18)° (y + 14…
\(x = 10\) \(m\angle M = 37^\circ\) \(m\angle N = 84^\circ\) \(m\angle P = 59^\circ\)
-
e) 1 : 10 a) 1 : 10 c) 5 : 9\t\tb) 1 : 3 e) 4 : 5\t\td) 7 : 10 state if…
### Problem 16: $\triangle JKL \sim \triangle JFG$ # Explanation: ## Step 1: Identify Angles In the diagram, $\angle KJL$ and $\angle FJG$ are vertical angles (so they are equal).…
-
trigonometry progress: the movement of the progress bar may be uneven b…
a = $\frac{7}{2}$, b = $\frac{7\sqrt{3}}{2}$
-
complete the proof that m∠u + m∠y = m∠wvy without using the triangle an…
For step 3, the reason is Alternate Interior Angles Theorem. For step 5, by substituting \( \angle U \) for \( \angle WVX \) and \( \angle Y \) for \( \angle XVY \) (from steps 2 …
-
complete the proof that ( mangle u + mangle y = mangle wvy ) without us…
Alternate Interior Angles Theorem
-
the polygons in each pair are similar. find the scale factor of the sma…
(Problem 14 and 15): 14) Let's recheck. The larger figure has 42, 24, 48. The smaller has 25, 20, and let's calculate 20/24 = 5/6, 25/30 = 5/6, 40/48 = 5/6, 35/42 = 5/6. So scale …
-
complete the proof that ( mangle g + mangle k + mangle ghk = 180^circ )…
For Statement 6, the reason is "Angles forming a linear pair sum to \( 180^\circ \)". For Statement 7, the reason is "Substitution Property (using \( m\angle IHK = m\angle G + m\a…
-
complete the proof that ( mangle g + mangle k + mangle ghk = 180^circ )…
- Step 2 Reason: Alternate Interior Angles Theorem - Step 4 Reason: Angle Addition Postulate
-
10. triangle with angles (11x - 1)°, (20x - 3)°, and an exterior angle …
For problem 10, \(x = 5\); for problem 11, \(x=7\)
-
14) write an equation of a line with a y-intercept of 2, but also make …
\( y = 5x+2 \)
-
uw ⊥ vw. complete the proof that m∠u + m∠v = 90°. (image of triangle uv…
For statement 2 (\(m\angle W = 90^\circ\)) the reason is "Definition of perpendicular lines (since \(\overline{UW} \perp \overline{VW}\), they form a right angle, so \(m\angle W =…
-
13) 99° (5x + 1)°
\(x = 16\)
-
8. (10x - 11)° (3x - 2)° (3x + 1)° 9. (3x - 5)° (7x + 5)°
Problem 8: \(x = 12\) Problem 9: \(x = 9\)
-
27. what elements can help you identify the tone of an informational ar…
the types of details used and word choices that affect style (the first option with the orange - filled circle)
-
complete the proof that ( mangle f + mangle j = mangle hgj ) without us…
For statement 4, the reason is "Additive Property of Angle Measure" (specifically the Angle Addition Postulate which is part of the Additive Property of Angle Measure, stating tha…
-
solve for x and circle your answer. -2(x - 8) = 20 (a) -2 (b) -10 (c) -…
(a) -2