Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
-
6 6.2.14 practice 6 find the surface area of the polyhedron that can be…
224
-
Question was provided via image upload.
- Slope (\(m\)): \(-3\) - Equation: \(y = - 3x-3\)
-
given the reference angle of \\(\\frac{2\\pi}{7}\\), find the correspon…
\(\frac{9\pi}{7}\)
-
roi and dating terms quiz review 1. mrs. hahn makes pencils and it cost…
$\$1.15$ ### Problem 2:
-
4) equation ordered pair = (-4,-3) ordered pair = (4,1) slope (m) = y-i…
- Slope (\( m \)): \(\frac{1}{2}\) - Equation: \( y=\frac{1}{2}x - 1 \)
-
7) equation ordered pair = (2,-4) ordered pair = (1,0) slope (m) = y-in…
- Slope (\(m\)): \(-4\) - Equation: \(y = - 4x+4\)
-
the entire rectangle below has an area of $52\\ \\text{ft}^2$. find the…
\( 26\space square\space feet \) (or \( 26\space ft^{2} \))
-
the shaded triangle has an area of $16\\ \\text{in}^2$. find the area o…
\( 32 \) square inches
-
3) equation ____________ ordered pair = __(-2,-4) ordered pair = __(-1,…
slope (\( m \)) = \( 3 \) equation: \( y = 3x+2 \)
-
what is the ratio of hexagons to triangles? options: 3 to 8, 8 to 3, 5 …
5 to 3
-
use the law of cosines. find length x. x = (round the final answer to o…
19.0
-
part 3 of 3 solve the triangle. (image of a triangle with side 5, side …
\(72.5\)
-
part 2 of 3 solve the triangle. (image of triangle with side 5, side 6,…
\(52.5\)
-
find the perimeter of the large triangle. options: 54, 12, 24, 36
36 (or the option with 36, e.g., 4. 36)
-
equation ordered pair = (3,0) ordered pair = (-3,2) slope (m) = y-inter…
- Equation: \( y =-\frac{1}{3}x + 1 \) - Slope (\( m \)): \( -\frac{1}{3} \)
-
part 1 of 3 solve the triangle. (image of a triangle with side 5, side …
\( 5.16 \)
-
estimate the measure of this angle within 15°. angle diagram and a rect…
\(30^\circ\) (or a value within \(15^\circ\) of \(30^\circ\), e.g., \(15^\circ - 45^\circ\) is acceptable, but \(30^\circ\) is typical)
-
in $\\triangle abc$, $ab = 30$, $ac = 23$, and $bc = 19$. what is $m\\a…
\( 39.3 \)
-
a golfer hits an errant tee shot that lands in the rough. a marker in t…
138.7
-
a golfer hits an errant tee shot that lands in the rough. a marker in t…
141.9
-
find the perimeter of the figure. (hint: recall that the perimeter of a…
$\boxed{\dfrac{22}{13}}$
-
part 3 of 3 solve the triangle. a = 3, b = 7, c = 10° c ≈ 4.1 (do not r…
\(163\)
-
equation ordered pair = (-4,-3) ordered pair = (-2,0) slope (m) = y-int…
Slope \( m=\frac{3}{2} \), Equation \( y = \frac{3}{2}x+3 \)
-
part 2 of 3 solve the triangle. a=3, b=7, c=10° c≈ 4.1 (do not round un…
\( 7 \)
-
part 1 of 3 solve the triangle. a=3, b=7, c=10° c ≈ (do not round until…
\(4.1\)
-
the figure is not to scale. which of the following additional statement…
B. Line $\boldsymbol{\ell}$ is parallel to $\overleftrightarrow{AB}$ only
-
solve each of the inequality for the variable below and graph your answ…
The solution to the inequality \(18 + 5x \leq 50 + 9x\) is \(x \geq -8\). To graph this, we draw a number line, place a closed circle at \(-8\) (since the inequality includes equa…
-
estimate the measure of this angle within 15°. (image of an angle with …
\(120^\circ\) (or other reasonable estimate within \(15^\circ\) of actual, e.g., \(105^\circ\), \(135^\circ\))
-
14. write an equation in standard form for a line with a slope of \\(\\…
$3x + 5y=-23$ ### Problem 15:
-
1) ordered pair = (4,4) ordered pair = (1,-2) equation slope (m) = y-in…
- Slope (\( m \)): \( 2 \) - Equation: \( y = 2x - 4 \)
-
estimate the measure of this angle within 15°. submit
\(45^\circ\) (or a value between \(30^\circ\) and \(60^\circ\), but \(45^\circ\) is typical)
-
draw the image of △abc under a dilation whose center is p and scale fac…
To draw the image: 1. Draw lines from \( P \) through \( A \), \( B \), and \( C \). 2. On each line, mark points \( A' \), \( B' \), \( C' \) such that the distance from \( P \) …
-
use the given information to prove that ∠qpr ≅ ∠spr. given: (overline{q…
Step 1: $\overline{QR} \cong \overline{SR}$ (Given) Step 2: $\overline{PQ} \cong \overline{PS}$ (Given) Step 3: $\overline{PR} \cong \overline{PR}$ (Reflexive Property) Step 4: $\…
-
3.11 rhombuses (or rhombi, if you like to be greek) 1. rhombuses have a…
(for Part 2 Proof): The proof uses the **SAS Congruence Postulate** with \(AC = DC\), \(\angle ACF = \angle DCF\), and \(CF = CF\). The table is filled as above. For Part 3, trian…
-
11. similar proofs: decide if each pair of triangles below is similar. …
a. The triangles are similar (by SSS similarity, as the ratios of corresponding sides are equal: \( \frac{8}{10}=\frac{9}{11.25}=\frac{12}{15}=\frac{4}{5} \)). b. The triangles ar…
-
graph the image of $\\triangle jkl$ after a rotation 90° counterclockwi…
### First Sub - Question (Graphing $\triangle JKL$ after transformation) #### Step 1: Identify coordinates of $\triangle JKL$ From the graph, we can see the coordinates: Let's ass…
-
line d has a slope of \\(\\frac{26}{17}\\). line e is parallel to line …
\(\frac{26}{17}\)
-
the equation of line d is $y = \\frac{-23}{67}x - \\frac{40}{15}$. the …
parallel
-
approaching solve each of the inequality for the variable below and gra…
The solution to \( -2 + 4x \geq -30 \) is \( x \geq -7 \). The graph has a closed circle at -7 and shading to the right.
-
line g passes through points (56, 31) and (70, 100). line h is parallel…
\(\frac{69}{14}\)
-
simplify your answer and write it as a proper fraction, improper fracti…
\(-2\)
-
the equation of line d is $y = \\frac{-7}{6}x + 7$. line e is parallel …
\(-\frac{7}{6}\)
-
the equation of line f is $y = \\frac{3}{8}x + 6$. the equation of line…
perpendicular
-
the equation of line d is $y = \\frac{-2}{9}x + 4$. the equation of lin…
perpendicular
-
the equation of line d is $y = \\frac{3}{4}x + 8$. line e is parallel t…
\(\frac{3}{4}\)
-
the equation of line g is $y = \\frac{3}{7}x + \\frac{1}{6}$. line h is…
\(-\frac{7}{3}\)
-
line m has a slope of \\(\\frac{-4}{9}\\). line n is perpendicular to m…
\(\frac{9}{4}\)
-
ions and perform the following rotations. b. rotate triangle abc 180° c…
### Part b: Rotate Triangle \( ABC \) \( 180^\circ \) clockwise about the origin #### Step 1: Identify coordinates of \( A \), \( B \), \( C \) From the graph (left): - \( A(-5, 3…
-
name 113 avoiding comma splices a comma splice occurs when two or more …
### Practice A: 1. I 2. C 3. I 4. I 5. I 6. C 7. I 8. C 9. I 10. C ### Practice B (sample answers): 1. Aunt Terri invited us to visit her in New York. Maybe we will go next summer…
-
name 113 avoiding comma splices a comma splice occurs when two or more …
For Practice A (example shown, let's do question 1 as an example): 1. The airport was crowded, a storm in Chicago closed the airport there. - I (circle the comma between "crowded"…
-
determine the relationship between the two triangles and whether or not…
The two triangles are related by a rotation (or congruence - preserving transformation), so the triangles can be proven to be congruent.
-
part one: read the instructions a. rotate triangle abc 90° clockwise ab…
The rotated triangle \( A'B'C' \) has vertices at \( A'(3, 5) \), \( B'(1, 2) \), \( C'(1, 5) \) (plotted on the coordinate plane as per the rotation rule).
-
12 joshua is constructing a triangle with a circle inscribed in it. eac…
D. incenter
-
question determine the relationship between the two triangles and wheth…
The two triangles are related by a rigid transformation (e.g., reflection), so the triangles can be proven congruent (by AAS/ASA congruence criteria).
-
8 what is the approximate length of the arc subtended by an angle of \\…
C. 25.13 meters
-
Question was provided via image upload.
The two triangles are related by \(\boldsymbol{\text{rotation}}\) (a rigid transformation), so the triangles \(\boldsymbol{\text{are congruent}}\).
-
7 the figure below shows concentric circles, both centered at o. what i…
B. 24 cm
-
14. toy rubber balls are packaged in a cylinder that holds 3 balls. fin…
\(773.6\) cubic centimeters (wait, no, wait, maybe I made a mistake. Wait, 3.45 squared is 11.9025, 11.9025*20.7=246.38175, 246.38175*3.14=773.638695, which is 773.6 when rounded …
-
3 the diameter of a circle is 8 centimeters. a central angle of the cir…
B. 3
-
question 24 (1 point) determine if the two triangles are congruent. if …
b. SAS
-
find the sum of the infinite geometric series. $5 - \\frac{5}{8} + \\fr…
\(\frac{40}{9}\)
-
date: 9-16-25 period: 6/4 unit 2 study guide point 6 name the figure us…
The length of the segment is approximately \(\boxed{6.32}\) (since \(2\sqrt{10}\approx 6.32\)).
-
find the sum of the first 13 terms of the geometric sequence. use the f…
\(1594324\)
-
which shows two triangles that are congruent by asa?
The first figure (the one with the triangle split by a perpendicular bisector showing congruent triangles via ASA due to two angles and the included side)
-
for exercises 1–5, use the diagram. 1. what composition of two rigid mo…
The coordinates of \( P' \) are \((-1, 3)\)
-
8 fill in the blank 4 points find x. triangle with two equal sides mark…
\( 75^\circ \)
-
analyzing translated graphs determine the vertex form of ( g(x) = x^2 +…
The graph on the right (the fourth graph) represents \( g(x)=x^2 + 2x - 1 \) (after converting to vertex form \( g(x)=(x + 1)^2 - 2 \) with vertex at \( (-1, -2) \)).
-
2. graph y = 2x + 5. a. b. c. d.
B. La gráfica de la opción B
-
4.1.5) graph the function on the coordinate plane below. include three …
(For graphing: The line passes through (0,3), (1,5), (-1,1), (2,7) with arrowheads. Right triangles as described. For mapping: x - values {-1,0,1,2} mapped to y - values {1,3,5,7}…
-
question 15 find the slope of the line going through the given pair of …
\(-2\)
-
find the length of the line segment between point a and point b. what i…
\(\sqrt{145}\)
-
find ab if f is the circumcenter of △aec, bf = 5.2, and fc = 12.7. roun…
\( 11.6 \)
-
use the right triangle abc to find the length of the line segment betwe…
\(\sqrt{97}\)
-
use the right triangle abc to find the length of the line segment betwe…
4
-
$\\overleftrightarrow{km}$ and $\\overleftrightarrow{np}$ are parallel …
$\angle MLJ$ and $\angle NOQ$ (the first option in the list of angle pairs)
-
use the right triangle abc to find the length of the line segment betwe…
The length of the line segment between point A and point C is 9.
-
use the right triangle abc to find the length of the line segment betwe…
\(\sqrt{130}\)
-
use the right triangle abc to find the length of the line segment betwe…
9
-
use the right triangle abc to find the length of the line segment betwe…
7
-
use the right triangle abc to find the length of the line seg you just …
The length of the hypotenuse (the line segment between \(A\) and \(B\)) is \(2\sqrt{41}\) (or approximately \(12.81\)).
-
now, find the exact length of the hypotenuse, c. thats the length of th…
\(\sqrt{164}\) (or \(2\sqrt{41}\))
-
maria was helping with the angles in the image below (given m∠7=25°). s…
The first explanation (the one stating "Minnie is partially incorrect because ∠2 and ∠3 are not vertical angles to ∠7. Instead, they are 35° because ∠2 is a congruent alternate ex…
-
use the right triangle abc to find the length of the line segment betwe…
$10^{2}+8^{2}=c^{2}$ (or $8^{2}+10^{2}=c^{2}$, where the first two boxes can be 10 and 8 (in any order) and the third box is c)
-
now, find the length of the other leg of this right triangle. what is t…
10
-
use the right triangle abc to find the length of the line segment betwe…
Length of AC: 8; Length of AB: $2\sqrt{41}$ (or approximately 12.81)
-
nina and rob were arguing about parallel lines cut by transversal quest…
Rob is correct. If you have one angle, you can fill in the congruent vertical, corresponding, and alternate interior/exterior angles and the supplementary linear pairs and consecu…
-
danny and gina both solved the following problem. is either of them cor…
Neither of them are completely correct. Danny set up the problem wrong, but his work is correct. Gina set up the problem correctly, but her work is wrong.
-
you just found the length of the hypotenuse, c. thats the length of the…
The length of the hypotenuse \(c\) is \(8\sqrt{2}\) (or approximately \(11.31\)).
-
use the right triangle abc to find the length of the line segment betwe…
\( 8\sqrt{2} \) (or approximately \( 11.31 \))
-
miguel solved the following problem below. is his work/answer correct? …
He set up the problem wrong, these angles are supplementary and he made algebra mistakes.
-
use the right triangle abc to find the length of the line segment betwe…
\(8\sqrt{2}\) (or \(\sqrt{128}\), but \(8\sqrt{2}\) is the simplified radical form)
-
jillong was tasked with identifying all the supplementary angles to ∠6 …
Her response is not fully correct, she said corresponding instead of consecutive interior and she said linear pair instead of adjacent interior angles.
-
use the right triangle abc to find the length of the line segment betwe…
\(8\sqrt{2}\)
-
find the value of x that makes j || k 13. 14. 15. 16. determine the mis…
\( x = 10 \) ### Problem 14:
-
on the map in the following figure, what is the distance between jordan…
a. 3 kilometers
-
ms/lti finding distances in the use the right triangle abc to find the …
8
-
note that wxyz has vertices w(-4, -4), x(-2, 3), y(y, 2), and z(-1, -5)…
(a) Length of \(\overline{WZ}\): \(\boldsymbol{\sqrt{10}}\), Length of \(\overline{XY}\): \(\boldsymbol{\sqrt{34}}\) (or correct based on \(Y\)’s actual coordinates). (b) Length o…
-
given the following, what is the value of x? image of two parallel line…
3
-
finding distances in the coordinate pla use the right triangle abc to f…
\(9^{2}+8^{2}=c^{2}\) (where the first box is 9, the second box is 8, and the third box is \(c\))
-
topic 4: rhombi & squares 21. if jklm is a rhombus, find each angle. 22…
\(m\angle STU = 112^\circ\)