Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
-
2. does a triangle with sides of lengths 1.5 ft, 2.5 ft, and 2 ft form …
Yes, because \(1.5^{2}+2^{2}=2.25 + 4 = 6.25\) and \(2.5^{2}=6.25\), satisfying the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).
-
in the figure, $overrightarrow{ca}$ and $overrightarrow{ce}$ are opposi…
$70^{\circ}$
-
the measures of two angles of a triangle are 66° and 62°. find the meas…
\(52^{\circ}\)
-
which statements are true about triangle abc and its translated image a…
The rule for the translation can be written as \(T_{3,-5}(x,y)\) The rule for the translation can be written as \((x,y)\to(x + 3,y-5)\) The triangle ABC has been translated 3 unit…
-
answer attempt 1 out of 2 x = y =
$x = 12$ $y = 120$
-
given (lparallel mparallel n), find the value of (x).
\(x = 18\)
-
2) given: ptom ≡ cbad grade 8: week of 9/22, math hw - day 2 directions…
\(PT = 41\mathrm{cm}\) \(DA = 50\mathrm{cm}\) \(TO = 79\mathrm{cm}\) \(CD = 112\mathrm{cm}\) \(m\angle B = 144^{\circ}\) \(m\angle O = 40^{\circ}\) \(m\angle M = 60^{\circ}\) \(m\…
-
in the figure, $overrightarrow{ca}$ and $overrightarrow{ce}$ are opposi…
D. $\angle GFC$
-
given m || n, find the value of x. answer attempt 2 out of 2 x =
\(x = 109\)
-
grade 8: week of 9/22, math hw - day 2 directions: show all steps of yo…
Rotate Polygon A 90 degrees counter - clockwise about a vertex and then translate it to match Polygon B.
-
graph the image of the figure using the transformation given. 9) reflec…
Graph the triangle with vertices obtained by applying the formula $(x,4 - y)$ to each vertex of the original triangle $STU$.
-
irina wants to tile her floor using the translation shown below. which …
\(T_{-3,2}(x,y)\)
-
find the measure of the missing angle. show all of your work.
For the first triangle, the missing - angle measure is \(81^{\circ}\). For the second triangle, the missing - angle measure is \(77^{\circ}\).
-
find the volume of a cone with a height of 10 ft and a base diameter of…
$94.2$ ft³
-
13. the average of your 3 quiz grades is 17 points. two of your quiz gr…
$20\frac{2}{3}$ feet ### 14.
-
a triangle on a coordinate plane is translated according to the rule t_…
C. $(x,y)\to(x - 8,y + 4)$
-
graph the image of the figure using the transformation given. 9) reflec…
Follow the above - mentioned steps to graph the reflected images for each transformation.
-
grade 8: week of 9/22, math hw - day 2 directions: show all steps of yo…
**Problem #1**: Rotate Polygon A 90 - degrees counter - clockwise about a vertex and then translate it to match Polygon B. **Problem #2**: The shapes are congruent. Translate Poly…
-
proof write a paragraph proof to prove that if e is the midpoint of $ov…
The proof is completed as shown above. We used the definition of a mid - point to establish equal - length segments and then used the substitution property of equality to prove th…
-
problem #5 - unit 1 (medium) a. find a shape congruent to shape a. b. n…
a. D b. C, E Problem #6: F
-
trapezoid lmnp was constructed using trapezoid lmnp. for the transforma…
A. \(LL' = PP'\) B. \(LL'=MM'\) C. Trapezoid \(LMNP\) is congruent to trapezoid \(L'M'N'P'\) E. All line segments that connect a point on the pre - image to its corresponding poin…
-
10. a custodian secures a ladder of l the school. the ladder makes an a…
The lower end of the lean - to should be approximately $1.48$ m away from the base of the tree. ### Question 12
-
which rule represents the translation from the pre - image, ▱abcd, to t…
$T_{1,2}(x,y)$
-
classify the triangles by angle measure. acute, obtuse, or right.
Acute; Obtuse; Obtuse; Acute
-
problem #5 - unit 1 (medium) a. find a shape congruent to shape a. b. n…
Problem #5 - a: D Problem #5 - b: C, E Problem #6: F
-
write a rule to describe each transformation. 5) 6) 7) 8)
5. $(x,y)\to(x - 2,y + 3)$ 6. $(x,y)\to(-x,-y)$ 7. $(x,y)\to(x,-y)$ 8. $(x,y)\to(x + 4,y - 2)$
-
the figure below is translated up 5 units. what are the coordinates of …
\((4,-3)\)
-
8. a 5 - m - long ladder is leaning up against the side of a barn. it r…
The angle the ladder makes with the ground is approximately $57.1^{\circ}$
-
the figure below is translated down 5 units. what are the coordinates o…
\((4,1)\)
-
the rule as a mapping for the translation of a rectangle is (x, y) → (x…
a translation of 2 units to the left and 7 units up
-
6 from unit 1, lesson 10 on the grid, draw three different triangles wi…
Draw three triangles on the grid: one with base 2 and height 8, one with base 4 and height 4, one with base 8 and height 2, and label the base and height of each.
-
the diameter of a cylindrical water tank is 12 ft, and its height is 13…
$1470$ ft³
-
the \golden rectangle\ is a rectangle that has the following ratio of w…
\(19.42\)
-
hexagon defghi is translated 8 units down and 3 units to the right. if …
B. $(-6,-6)$
-
3. find x to the nearest tenth of a centimetre. a) b)
a) $25.6$ cm b) $8.0$ cm
-
53. geometry the width of a box is 2 m less than the length. the height…
5 m
-
rectangle efgh is translated according to the rule t_{-5,9}(x,y). if th…
B. $(-7,6)$
-
8. the length of a rectangle is nine more than twice the width. write a…
$6w + 18$
-
classify the triangles by side length. equilateral, isosceles, or scale…
1. Scalene 2. Scalene 3. Isosceles 4. Isosceles
-
a triangle on a coordinate plane is translated according to the rule $t…
A. $(x,y)\to(x - 3,y + 5)$
-
a rectangle is drawn so the width is 5 inches longer than the height. i…
$24.2$
-
the image of the figure using the transformation given. reflection acro…
To find the image of a figure reflected across $x = 2$, use the rule $(x,y)\to(4 - x,y)$ for each point $(x,y)$ of the original figure.
-
grade 8: week of 9/22, math hw - day 1 directions: show all steps of yo…
1. $\overline{XZ}$, $\angle Q$ 2. $\angle A$, $\overline{XY}$ 3. $\overline{DB}$ 4. a. A b. D and F
-
using the transformation given. 4) reflection across x = 2
A point $(x,y)$ is reflected to $(4 - x,y)$ across the line $x = 2$.
-
6. what is the solution of the equation below? 0.1(20x + 100)=3x + 10 (…
A. \(x = 0\)
-
practice problems from unit 1, lesson 9 a. identify a base and a corres…
a. Base $b = 6$ units (horizontal side), height $h = 2$ units (perpendicular distance from base to opposite vertex) b. 6 square units
-
proof complete the flow proof to prove that if point m is the mid - poi…
Drag "LM = MN" to the first blank under "M is the mid - point of LN, L is the mid - point of AB, AL = MN" using the mid - point theorem. Drag "AL = LB" to the second blank under t…
-
graph the image of the figure using the transformation given. 3) reflec…
# Explanation: ## Step1: Recall reflection formula For a point $(x,y)$ reflected across the vertical line $x = a$, the new - point $(x',y')$ is given by the formula $x'=2a - x$ an…
-
5 from unit 1, lesson 9 a. identify a base and a corresponding height t…
a. Base $b = 8$ units, height $h = 3$ units (answers may vary depending on which side is chosen as the base). b. The area of the triangle is 12 square - units.
-
for help with question 1, refer to example 1. 1. use a scientific calcu…
# Explanation: ## Step1: Use scientific - calculator for sine and cosine values Use a scientific calculator to find the sine and cosine of the given angles and round to four decim…
-
initial knowledge check question 8 congruent? yes no similar? yes no co…
Top - left: Congruent? No, Similar? No Top - right: Congruent? Yes, Similar? Yes Bottom - left: Congruent? No, Similar? Yes Bottom - right: Congruent? Yes, Similar? Yes
-
28. miriam is sewing an appliqué of an ice cream cone on a flag which t…
Approximately 220 square inches.
-
which pairs of figures below are congruent?
First pair: No Second pair: No Third pair: Yes Fourth pair: No
-
lin and andre used different methods to find the area of a regular hexa…
Using Lin's method, the area is approximately \(93.528\) square inches. Using Andre's method, the area is approximately \(93.528\) square inches.
-
how many lines of symmetry does this quadrilateral have? a) 4 b) 2 c) 1
b) 2
-
for the parabola graphed below, identify its vertex, axis of symmetry, …
The vertex of the parabola is $(0,5)$ The axis of symmetry is $x = 0$ The parabola opens downwards
-
which parts of figures below are congruent? congruent? yes no yes no co…
First pair: No Second pair: No Third pair: Yes Fourth pair: No
-
4. mp.1 make sense sort shapes a - j into two or more piles based on si…
There are multiple ways to sort such as by number of sides or shape type, but specific sorting depends on the actual shapes A - J.
-
12. a ladder leans against a vertical wall and makes an angle of 76° wi…
$7.2$ m
-
how many lines of symmetry does this quadrilateral have? a) 3 b) 1 c) 2
c) 2
-
10. write a similarity statement for the similar triangles. (\triangle …
NQR
-
4. find the distance from the boat to the base of the lighthouse, to th…
51 m
-
find the area of this trapezoid. explain or show your strategy.
15 square units
-
8. the triangles are similar by the aa similarity postulate. find the v…
2.5
-
write an equation of the line. 25. 26. 27.
The equation of the line is $y = mx + b$, where $m=\frac{y_2 - y_1}{x_2 - x_1}$ and $b=y_1 - mx_1$ for two points $(x_1,y_1)$ and $(x_2,y_2)$ on the line.
-
7. write a similarity statement for the similar triangles. △lmn∼△____ q…
A. QRS
-
11 practice problems 3 find the area of this trapezoid. explain or show…
15 square units
-
6. select the postulate or theorem that you can use to conclude that th…
AA Similarity Postulate
-
performance assessment puzzle pieces laura is sorting her puzzle - piec…
2. A, D, E, F, G 3. A, B, D, E, F, G, H, J
-
1. use a scientific calculator to find each value to four dec a) tan 28…
1. a) $\tan28^{\circ}\approx0.5317$ b) $\tan36^{\circ}\approx0.7265$ c) $\tan45^{\circ}=1.0000$ d) $\tan72^{\circ}\approx3.0777$ 2. a) $A=\tan^{-1}(0.3443)\approx19^{\circ}$ b) $A…
-
1. the triangles are similar by the aa similarity postulate. find the v…
12
-
4. the triangles are similar by the aa similarity postulate. find the v…
15
-
3. select the postulate or theorem that you can use to conclude that th…
SAS Similarity Theorem
-
all of these shapes are rectangular prisms. circle the words that are t…
have 12 edges, have 6 faces
-
2. the triangles are similar by the aa similarity postulate. find the v…
9
-
2. the triangles are similar by the aa similarity postulate. find the v…
9
-
2 mark each vertex with a large dot. how many edges and vertices does t…
Vertices: 12; Edges: 12
-
find the volume of a box that will hold six 150.8 in³ cylindrical conta…
A. 905 in³
-
1 select all the polygons.
A. The arrow - shaped figure, C. The star - shaped figure, D. The triangular figure
-
the perimeter of a rectangle is given by the formula $p = 2l + 2w$, whe…
C. $w=\frac{P - 2l}{2}$
-
for each pair of shapes, decide whether or not shape a is congruent to …
Yes. A translation can be used to show congruence. We know this because translations are rigid - motion transformations that preserve the size and shape of a figure, and by observ…
-
for each of the following pairs of shapes, decide whether or not they a…
Yes. The two octagons are congruent. A translation can move one figure to the other.
-
solve and graph. |x - 1| < 15. write the solution using set - builder n…
The solution in set - builder notation is \(\{x|-14\lt x\lt16\}\). The graph would be a number line with an open circle at \(x=-14\) and an open circle at \(x = 16\), and the line…
-
for each of the following pairs of shapes, decide whether or not they a…
Yes. The two triangles are congruent. A rotation followed by a translation will move one figure to the other.
-
guided practice: rearrange formulas the formula for the area of a trian…
1. Multiply both sides by 2. 2. Divide both sides by h. 3. $b=\frac{2A}{h}$
-
the perimeter of a triangle is given by the formula p = a + b + c. solv…
B. $P - a - c$
-
for each set of three measures, determine if they can be angle measures…
(a) Cannot be angle measures of a triangle (b) Can be angle measures of a triangle (c) Cannot be angle measures of a triangle (d) Cannot be angle measures of a triangle
-
find the volume of a box that will hold nine 9.425 cm³ cylindrical cont…
85
-
in the figure below, m∠2 = 77°. find m∠1, m∠3, and m∠4.
$m\angle1 = 103^{\circ}$ $m\angle3 = 103^{\circ}$ $m\angle4 = 77^{\circ}$
-
20. a right - triangle has one acute angle that measures 38°. find the …
The measure of the third angle is 52°, and the triangle is scalene.
-
2 a geometry teacher distributes sheets of construction paper to her cl…
2(a): $V(x)=4x^{3}-84x^{2}+432x$ 2(b): $x = 8$ 2(c): $x = 3$, Volume = $648$ cubic inches, Dimensions: length = $18$ inches, width = $12$ inches, height = $3$ inches 3(a): $g(x)=x…
-
draw a line representing the “rise” and a line representing the “run” o…
$-\frac{5}{8}$
-
lesson 3 9 - 30 performing sequences of rigid transfo perform the given…
For the first set of transformations (reflect across x - axis and translate 5 units left): The final image is congruent to the original figure. General new coordinates of a point …
-
determine which translations would map figure n onto figure o. press \t…
A translation 0 units horizontally and - 8 units vertically.
-
use the number sentences to draw a picture, and fill in the number bond…
1. In the number - bond: left squares have 5 and 2, right square has 7. Picture: 5 circles and 2 circles combined. 2. In the number - bond: left squares have 3 and 6, right square…
-
determine which translations would map figure n onto figure o. press \t…
A translation left 8 units and 0 units down (or up).
-
given m||n, find the value of x. (4x - 8)° (7x - 20)° answer attempt 1 …
\(x = 4\)
-
6. find the measure of each angle. a. ∠1 and ∠2 form a linear pair and …
a. $m\angle1 = 128^{\circ}$ b. $m\angle4 = 132^{\circ}$
-
5. complete the reasons for the 2 - column proof. given: ∠1 and ∠2 are …
1. Given 2. Definition of complementary angles 3. Definition of complementary angles 4. Vertical - angles are congruent 5. Definition of congruent angles 6. Transitive property of…
-
if a translation of $t_{2,-7}(x,y)$ is applied to $\triangle abc$, what…
$(3, - 12)$