Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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1. if two parallel lines are cut by a transversal, what is the relation…
1. The measures of corresponding angles are equal (congruent). 2. Alternate interior angles formed by parallel lines are congruent. 3. The two lines are parallel. 4. 115°
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two angles that add to 90° are called: supplementary angles obtuse angl…
D. complementary angles
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in the diagram below, $overline{ab}paralleloverline{df}$, $mangle dce =…
$75^{\circ}$
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129° 1 95° 47° 5 7 121° 2 6 47 38 133 129
$47$
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4. if c, p, and t are the mid - points of the sides of △aen, pt = 13, e…
a) \(AE = 26\) b) \(AN = 58\) c) \(CT = 21.5\) d) Perimeter of \(\triangle AEN=127\)
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scale drawings a and b are made from the same original drawing. scale d…
a. The scale factor relating scale - drawing B to scale - drawing A is 12. b. First, find the area of the kitchen in scale - drawing A. Then multiply this area by the square of th…
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the center of a circle is at the origin on a coordinate grid. the verte…
The circle has a radius less than 9.
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which word describes angles that have the same relative position on two…
corresponding angles
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check out this cube: find the surface area of the cube (above) using it…
54
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129° 95° 47° 121° 47 95 85 133
133
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find the coordinates of the point 3/10 of the way from a to b. the coor…
\((-2.6,1.3)\)
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uation for the line below.
$y=\frac{2}{3}x+\frac{7}{3}$
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the vertex of a parabola is in the first quadrant of a coordinate grid.…
The parabola opens upward.
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10. find all missing angles. find all missing angles. 72° 57° 1 2 3 4 9…
18
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9. find all missing angles. m - 2 1 72° 57° 3 2 4 o 9 o 45 o 90 o 18
18
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if 1/5 of a 90 - degree angle 1 72° 57° 3 2 4 9 45 90 18
18
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consider the following system of equations. \\(\\begin{cases}- 10x^{2}-…
The equations represent circles that result in the same graph.
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5. find all missing angles. 1 72° 57° 3 2 4 57 72 51 75
75
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find the surface area of the square pyramid (above) using its net (belo…
12
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graph the line y = 8.
Draw a horizontal line passing through the point $(0,8)$ on the y - axis.
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4. if g is the mid - point of ab, classify each triangle by its angles …
obtuse, scalene
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graph the line y = 8.
Draw a horizontal line passing through the point $(0,8)$ on the $y$-axis.
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3. if g is the mid - point of ab, classify each triangle by its angles …
acute, scalene
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what is the theoretical probability of randomly picking a circle from t…
$\frac{1}{3}$
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2. if g is the mid - point of ab, classify each triangle by its angles …
acute, isosceles
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1. if g is the mid - point of ab, classify each triangle by its angles …
right, scalene
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find the perimeter and area of the figure below. figure is not drawn to…
713
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the perimeter of a 6 - sided figure is 67.74 meters. two of the sides h…
15.5
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draw a line representing the “rise” and a line representing the “run” o…
-1
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example 3 translate each sentence into an equation or formula. 9 twice …
9. $2a + a^{3}=b$ 10. $(p + t)-7 = 6$ 11. $x + x^{2}=yz$ 12. $4(f + g)=6g$ 13. $A=\ell^{2}$ 14. $P=a + b + c$
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question 3 of 10 solve the inequality for x and identify the graph of i…
D. Solution: \(x>-4\) and \(x < 0\) (the corresponding graph with open - circles at \(-4\) and \(0\) and the line segment between them shaded)
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given m || n, find the value of x.
\(x=\frac{86}{9}\)
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problem 2: rotate a right triangle 180°. what happens to the right angl…
The right - angle remains a right - angle.
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given m||n, find the value of x. (2x - 29)° (10x + 5)° answer x =
\(x = 17\)
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8th grade math geometry study guide 8.g.1.b - angles map to angles of t…
\(75^{\circ}\)
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given m || n, find the value of x. 103° x°
\(77\)
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8. a. solve the given inequality. b. describe the solution - set using …
a. Solution: \(b>11\) b. Set - builder notation: \(\{b|b > 11,b\in\mathbb{R}\}\) c. On the number line, mark an open - circle at 11 and shade to the right.
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given m||n, find the value of x.
\(x = 100\)
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in the diagram below, $overline{ad}paralleloverline{eg}$, $overline{bh}…
59°
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in the diagram below, $overline{ad}paralleloverline{eg}$, $overline{bh}…
31°
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problem 6: state a rule that shows segments remain congruent after rota…
A rotation is a rigid motion, and rigid motions preserve distance. So, if a segment has a certain length before rotation, its length remains the same after rotation, meaning the p…
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3.3 practice with calcchat and calcview® in exercises 1 - 6, find the v…
1. **Ejercicio 2**: - **Explicación Paso - 1**: Sabemos que si \(m\parallel n\), entonces los ángulos correspondientes son iguales. Aquí, los ángulos \((2x + 15)^{\circ}\) y \(135…
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for each shape below, find x. (a) perimeter = 38cm (b) perimeter = 30cm…
(a) $x = 6$ (b) $x = 6$ (c) $x = 12.5$ (d) $x = 8$ (e) $x = 1$ (f) $x = 20$
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in △hij, m∠h = 30° and m∠i = 29°. which statement about the sides of △h…
HI > IJ > HJ
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question in △rst, m∠r = 44° and m∠s = 98°. which list has the sides of …
RS, TR, ST
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8th grade math geometry problem 4: explain why translations preserve se…
Translations are rigid - motions that do not change distances between points, so segment lengths are preserved. Dilations with \(k eq1\) change distances between points by multip…
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for what values of x and y are the triangles to the right congruent by …
$x = 11$ and $y = 4$
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problem 3: rotate △xyz 180°. verify xy = xy. rotate about origin answer:
The lengths $XY$ and $X'Y'$ are equal because a 180 - degree rotation about the origin is a rigid - motion transformation which preserves distances. Mathematically, using the dist…
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for what values of x and y are the triangles to the right congruent by …
$x = 10$ and $y = 4$
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find the surface area:
\(142\mathrm{cm}^2\)
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study the example showing how to use multiples to solve a word problem.…
1. Circled numbers on number - line: 4, 8, 12, 16, 20 2. Example multiplications: 4×7 = 28, 4×8 = 32, 4×9 = 36, 4×10 = 40 3. No, there are infinitely many multiples of 4 such as 4…
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b. can it also be proved that $overline{pq}congoverline{rs}$ if $overli…
Yes, the Segment Addition Postulate can be used to show that $PR = PQ+QR$ and $QS = QR + RS$. Both equations can be solved for $QR$, and substituting $PR - PQ$ for $QS - RS$ (sinc…
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whats the surface area of a cube with a side length of 5 inches? a 150 …
A. 150
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21. you run the perimeter of the rectangular soccer field. how far do y…
347.16 m
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find the surface area of the square pyramid: 8 cm 5 cm
$105$ $cm^{2}$
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focus on nouns a noun is a word that names a person, place, thing, or i…
**A. Concrete Nouns** 1. socks 2. belt 3. scarf 4. shirt 5. musician 6. clerk **Abstract Nouns** 7. laziness 8. sweetness 9. fame 10. pain 11. confidence 12. bravery **B. Nouns in…
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find the surface area of the square pyramid.
105 cm²
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two parallel lines are cut by a transversal as shown below. suppose m∠8…
\(m\angle1 = 126^{\circ}\) \(m\angle3 = 126^{\circ}\)
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19. generalize a graphic designer wants to know the number of regions t…
La regla es $R(n)=n^{2}-n + 1$, y el número de regiones para $6$ círculos es $31$.
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whats the surface area of a cube with a side length of 5 inches? a. 150…
A. 150
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two parallel lines are cut by a transversal as shown below. suppose m∠4…
$m\angle6 = 103^{\circ}$ $m\angle7 = 77^{\circ}$
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what is the name of this figure? a. unclear b triangular prism c cube d…
B. Triangular Prism
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exponential relationships module goal: students will learn about geomet…
Option 2 is better since the amount of money after 30 days of doubling a penny each day is $\$5368709.12$, which is more than $\$1000000$ in Option 1.
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for the following right triangle, find the side length x. round your an…
$15$
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for the following right - triangle, find the side length x. round your …
\(10.58\)
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spiral review 7. here is an unlabeled rectangle and several quadrilater…
| | A | B | C | D | E | F | G | H | |---|---|---|---|---|---|---|---|---| | Is it a scaled copy? | No | Yes | Yes | Yes | Yes | No | Yes | Yes | | Scale Factor | - | 2 | 1.5 | 0.5…
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15. a 12 - inch tall model casts a shadow of 4 inches. a full - scale o…
d. 48 feet
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find the surface area:
$62$ $cm^{2}$
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14. a building casts a shadow 50 ft long, and a 5 ft pole casts a shado…
B. Set up a proportion using similar triangles.
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13. if triangle a has side lengths of 4, 5, and 6, and triangle b has s…
2
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12. if triangles acd and xyz are similar by the aa criterion, what can …
a. They are proportional.
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11. which transformation changes the size of a figure but preserves its…
a. Dilation
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10. in △abc, ∠acb = 90°, and cd is the altitude to ab. if ac = 5, bc = …
d. 4.6
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proving a theorem give the reasons for the proof of consecutive interio…
1. Given 2. Linear - pair postulate 3. Definition of supplementary angles
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9. a triangle has vertices a(1,2), b(3,4), and c(2,6). after a transfor…
c. \((x + 3,y + 3)\)
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find the surface area:
$239.4$ $cm^{2}$
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8. in △abc, ∠acb = 90°, and cd is the altitude to ab. which of the foll…
b. $\triangle ACD\sim\triangle ABC\sim\triangle BCD$
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7. what is the length of the hypotenuse of a right triangle with legs m…
a. 25 units
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find the value of x that makes m || n.
$x = 20$
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6. a pentagon with vertices p(1,2), q(3,2), r(4,4), s(2,5), and t(0,4) …
d. \((x + 2,y + 2)\)
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5. in proving triangle similarity, which pair of angles are always equa…
d. Corresponding angles
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4. a tree and a pole cast shadows at the same time. what property allow…
b. Their shadows form similar triangles.
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multiple - choice question what is the last linear pair in this diagram…
There is not enough information to determine the answer as the diagram is not provided.
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statements reasons 1. $overrightarrow{ba}perpoverrightarrow{bc}$ 1. giv…
The proof shows that if $\overrightarrow{BA}\perp\overrightarrow{BC}$, then the two non - overlapping angles $\angle 1$ and $\angle 2$ that make up $\angle ABC$ are complementary.
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15. can you find a counterexample for the following statement? a trapez…
# Explicación: ## Paso 1: Analizar el patrón Observamos que para 1 círculo hay 1 región, para 2 círculos hay 3 regiones, para 3 círculos hay 7 regiones y para 4 círculos hay 13 re…
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3. a rectangle with vertices p(1,1), q(3,1), r(3,4), and s(1,4) is dila…
2
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4. how many lines of symmetry does an equilateral triangle have?
3
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decide whether there is enough information to prove m||n. if so can use…
Yes, can use Corresponding Angles Converse to prove \(m\parallel n\)
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rotate the polygon 180° about the origin.
Plot the polygon with vertices obtained by applying the rule $(x,y)\to(-x,-y)$ to the original polygon's vertices.
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4. which of these lettered figures goes in the white space?
B. Option B
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structure in the diagram, a⊥b . find the value of x that makes b||c .
\(x = 8\)
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question 3 of 14, step 2 of 2 consider the following linear inequality.…
The solution set is \(p>-\frac{3}{2}\), and on the number - line, an open circle at \(-\frac{3}{2}\) and an arrow to the right.
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find the value of x that makes m || n. 135° (2x + 15)° m n x =
60
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in 6 and 7, use the table at the right. 6. © mp.4 model with math how m…
La estimación es 600 y la suma exacta es 597. ### 7.
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construction you are given $overline{ab}$ as shown. you are asked to us…
The diagram that shows arcs drawn from both endpoints $A$ and $B$ of the line - segment $\overline{AB}$ (with equal compass width) above and below the line - segment and then a li…
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2. draw two polygons that are similar but could be mistaken for not bei…
Draw a rectangle with side - lengths 2 and 4 and another rectangle with side - lengths 4 and 8. They are similar because corresponding angles are equal (all 90 degrees) and the ra…
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are $overleftrightarrow{ac}$ and $overleftrightarrow{df}$ parallel? exp…
yes; By the Vertical Angles Congruence Theorem, $m\angle EBC = 115^{\circ}$. So, consecutive interior angles are supplementary, and $\overleftrightarrow{AC}$ and $\overleftrightar…
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find the surface area of this box: 8\ h 12\ w 16\ l
$832$ square inches
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do you understand? do you know how? 1. essential question what is slope…
1. **What is slope?** - # Brief Explanations: - Slope measures the steepness of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) …
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8. error analysis danielle tests the following conjecture. if two angle…
Danielle olvidó que los ángulos adyacentes deben tener un lado común además de un vértice común.