Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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given: ab is the height of the cone. a plane, parallel to the base of a…
$9\pi$ square inches
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this rectangular prism is cut by the plane shown. the plane is perpendi…
A. rectangle.
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what is the area of the irregular pentagon? (image of an irregular pent…
$96 + 9 = 105$ square inches
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all sides of quadrilateral (abcd) are tangent to circle (p). what is th…
40
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all sides of quadrilateral abcd are tangent to circle p. what is the pe…
# Explanation: ## Step1: Recall Tangent Segments Property For a quadrilateral tangent to a circle (a tangential quadrilateral), the lengths of the two tangent segments from a sing…
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25. the equation $4x^2 + 4y^2 = 36$ represents which conic section? - e…
B. circle
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the following passage (paragraph 4) mainly shows that ________. a frien…
C. there’s no reason to panic, because the younger generation will probably lose that attitude as they age
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24 an ellipse has a vertex at (5, 0), a co - vertex at (0, - 3), and a …
$\boldsymbol{\frac{x^2}{25}+\frac{y^2}{9}=1}$
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22 write an equation of a parabola that opens upward, has a vertex at t…
$\boldsymbol{y=\frac{1}{8}x^2}$
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22 write the equation of the ellipse with its center at the origin. the…
$\frac{x^2}{64} + \frac{y^2}{16} = 1$
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21. graph the hyperbola \\(\\frac{x^2}{25} - \\frac{y^2}{49} = 1\\). wh…
(±5, 0)
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20. find the center and radius of the circle with equation ((x - 6)^2 +…
center (6, -5); radius 3
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19. identify the vertex, focus, and directrix. $x = -\\frac{1}{28}y^2$ …
vertex (0, 0); focus (-7, 0); directrix at x = 7
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79. if a rectangle measures 54 meters by 72 meters, what is the length,…
90 ### Problem 80:
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18. graph the hyperbola $\frac{y^2}{16} - \frac{x^2}{9} = 1$ what are t…
B. $\pm 4$
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17 what is the equation for the translation of ( x^2 + y^2 = 25 ) two u…
$\boldsymbol{(x + 2)^2 + (y + 4)^2 = 25}$
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16. what is the equation for the translation of (x^2 + y^2 = 16) seven …
A. $(x - 7)^2 + (y - 5)^2 = 16$
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15 what is the equation of the conic section? options: $x^2 + 9y^2 = 9$…
A. $x^2 + 9y^2 = 9$
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14. the equation $y^2 - x^2 = 1$ represents which conic section? hyperb…
A. hyperbola
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6. which of the following sets of lengths could be used to form a right…
6. A. 39 cm, 15 cm and 36 cm 7. C. Because $2^2 + 4^2 eq 7^2$ 8. 15 inches 9. $25 \text{ cm}^2$ 10. Yes, because $9^2 + 12^2 = 15^2$, which satisfies the Pythagorean theorem. 11…
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13 graph the hyperbola \\(\\frac{y^2}{16} - \\frac{x^2}{9} = 1\\) what …
(0, ±4)
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10. what are the x-intercepts of the ellipse? (with a coordinate grid a…
$\pm 3$ (o los puntos $(3, 0)$ y $(-3, 0)$)
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quadrilateral ghlj is similar to quadrilateral klmn. find the measure o…
48.4
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9. the equation $25x^2 + 25y^2 = 125$ represents which conic section? o…
circle
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8. find the center and radius of the circle with equation ((x + 8)^2 + …
center (-8, -3); radius 7
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quadrilateral lmno is similar to quadrilateral pqrs. find the measure o…
The measure of side PQ is approximately \(42.1\).
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quiz 1 date ______ pd ______ quiz: pythagorean theorem show all work as…
1. D. $84^2 + 56^2 = c^2$ 2. 7 ft 3. 13.4 in 4. B. (Triangle with right angle between sides $b$ and $c$, hypotenuse $a$) 5. 28 feet
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6. an ellipse has a vertex at (2, 0), a co - vertex at (0, - 1), and a …
$\boldsymbol{\frac{x^2}{4} + \frac{y^2}{1} = 1}$ (la tercera opción)
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10. find \\(\\overline{xk}\\). 1. a video game designer is modeling a t…
\( \overline{XK}=9 \) ### Problem 1: Video Game Model (Assuming the tower's height is missing, let's assume the tower's height is \( H \) ft and width is 240 ft, similarity ratio …
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5. write an equation of an ellipse in standard form with the center at …
$\boldsymbol{\frac{x^2}{90.25} + \frac{y^2}{36} = 1}$ (corresponde a la primera opción de la imagen)
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4. what is the equation of a circle with center (3, 8) and radius 2? (x…
C. $(x - 3)^2 + (y - 8)^2 = 4$
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4. determine whether the following points are on the line represented b…
a) Yes; b) Yes
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2. write an equation for a parabola in which the set of all points in t…
$\boldsymbol{x = -\frac{1}{8}y^2}$ (corresponding to the option: $\boldsymbol{x = -\frac{1}{8}y^2}$)
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1 write an equation of a parabola that opens to the left, has a vertex …
A. $x = -\frac{1}{36}y^2$
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45-45-90 triangles practice (first triangle: right - angled, one angle …
Let's solve each 45-45-90 triangle problem. Recall that in a 45-45-90 triangle, the legs are equal, and the hypotenuse \( h = \text{leg} \times \sqrt{2} \), or \( \text{leg} = \fr…
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the catching of unshelled fish (one simon (mythic game)) 1 unshell fish…
C. The real angler will sit all day in a boat in a pouring rain, intently watching the point of the rod, which never for an instant ceases a half inch from the horizontal.
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30-60-90 triangle practice first triangle: right triangle, hypotenuse 1…
Let's solve each 30 - 60 - 90 triangle problem one by one. Recall the properties of a 30 - 60 - 90 triangle: the sides are in the ratio \(1:\sqrt{3}:2\), where the side opposite \…
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find both variables 1. 2. 3. 4. 5. 6. 7. 8. jen is on the platform of h…
1. $a=6$, $b=3\sqrt{3}$ 2. $d=2$, $c=2\sqrt{3}$ 3. $f=8\sqrt{3}$, $e=16$ 4. $i=\frac{10\sqrt{3}}{3}$, $h=\frac{20\sqrt{3}}{3}$ 5. $j=4\sqrt{3}$, $k=8$ 6. $t=3\sqrt{3}$, $r=6\sqrt{…
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9. what is the equation of a hyperbola with a = 8 and c = 20? assume th…
# Explicación: ## Paso 1: Recordar la relación de la hipérbola Para una hipérbola con eje transversal horizontal, se cumple $c^2 = a^2 + b^2$, donde $a$ es el semieje transversal,…
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what is the ordered pair for point a? (\\boxed{?}, \\boxed{})
$(2, 1)$
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7. what is the equation of a hyperbola with a = 1 and c = 9? assume tha…
$\boldsymbol{x^2 - \frac{y^2}{80} = 1}$ (corresponding to the last option)
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in triangle abc, the altitude, \\(\\overline{cd}\\), is labeled \\(h\\)…
| Statements | Reasons | |------------|---------| | $\sin A = \frac{h}{a}$; $\sin B = \frac{h}{b}$ | Definition of sine | | $h = a\sin A$; $h = b\sin B$ | Multiplication property …
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illustrative mathematics - geometry 3. in triangle abc (not a right tri…
The area of triangle \( ABC \) equals \( \frac{1}{2}h \cdot c \).
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2. in right triangle abc, altitude cd with length h is drawn to its hyp…
\( 6 \)
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circle the following words, names and expressions in the letter grid. t…
Located items from the grid: 1. pique-nique (row 5, forward: P I Q U E N I Q U E) 2. football (row 3, forward: F O O T B A L L) 3. Louvre (row 14, forward: L O U V R E) 4. nager (…
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answer questions 8 - 10 and be sure to show all work. 8. find the later…
8. $\boldsymbol{119.38\ \text{cm}^2}$ 9. $\boldsymbol{1820.53\ \text{mm}^2}$ 10. Lateral surface area: $\boldsymbol{77.7\ \text{in}^2}$ Total surface area: $\boldsymbol{109.6\ \te…
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find the value of that represents each trig ratio. leave your answer as…
| Ratio | Simplified Fraction | Decimal | |---------|---------------------|----------| | 4. $\sin A$ | $\frac{24}{25}$ | $0.96$ | | 5. $\cos A$ | $\frac{7}{25}$ | $0.28$ | | 6. $\…
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use the parallelogram to find m∠bad. m∠bad = 102°
$102^\circ$
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use the parallelogram to find m∠bad. m∠bad = \\(\\square^\\circ\\)
\(102\)
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use the parallelogram to find $m\\angle bad$. $m\\angle bad=\\square^\\…
$84$
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question 1-30 text of the question is partially visible, with some part…
Direct
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find the measure of the numbered angles in the parallelogram. m∠1=□° m∠…
$m\angle 1 = 28^\circ$ $m\angle 2 = 27^\circ$ $m\angle 3 = 27^\circ$
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geometry quiz (b): pythagorean theorem and trig directions: show all wo…
1. $7$ 2. $17$ 3. a) (Square with side length $s$ and diagonal labeled 30 meters) b) $15\sqrt{2}$ meters (or approximately 21.21 meters) c) $60\sqrt{2}$ meters (or approximately 8…
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find the length of the hypotenuse of the right triangle drawn on the co…
9.4
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14. given the inequality (4x + 2 < -2), (x < -1)\ 14b which of the numb…
The number line with an open circle at \(-1\) and the line shaded to the left (e.g., the one labeled as the correct representation for \(x < -1\) among the options, likely the fir…
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1 find slope of given points (-3, 4) (4,6) 2 (-2, 3) (8,3)
1. Slope of $(-3,4)$ and $(4,6)$: $\frac{2}{7}$ 2. Slope of $(-2,3)$ and $(8,3)$: $0$
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10) $\\frac{n}{3} > 3$ (and a number line with marks at 3, 4, 5, 6, 7, …
$n > 9$ (On the number line, draw an open circle at 9 and shade all values to the right of 9.)
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12. what is the value of x? (4x + 5)° (8x - 6)°
$x = \frac{181}{12}$ or approximately $15.08$
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9) -3x > 3
$x < -1$ (Graph: Open circle at -1, arrow extending left along the number line)
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learning targets - i can visually determine if two lines are perpendicu…
B and C (the rectangle and the right triangle) ### Question 2:
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6) $15 + x \\leq 0$
The solution to the inequality is $x \leq -15$. The correct number line representation has a closed circle at -15 and an arrow extending to the left (toward smaller numbers). The …
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5) a - 17 ≥ -16
$a \geq 1$ (On the number line, this is represented by a closed circle at 1 and an arrow pointing to the right, which matches the given number line illustration.)
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a companys logo a company’s logo is represented in the figure on the ri…
1. Equation of line $l$: $\boldsymbol{y=5}$ 2. Equation of parabola $g$: $\boldsymbol{y = -\frac{1}{8}(x-6)^2 + 2}$ (or expanded: $\boldsymbol{y = -\frac{1}{8}x^2 + \frac{3}{2}x -…
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2. zilan wil vier punten a, b, c en d in het vlak zetten zodat |ab| = 4…
B. 6 ### Question 3
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construction - copying a segment construct a segment whose length is eq…
The constructed segment is $\overline{DE}$, which has the same length as $\overline{YZ}$.
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9. ∠a and ∠b are supplementary. if m∠a = (5x − 1)°, and m∠b = (5x + 21)…
$x = 16$ $m\angle A = 79^\circ$ $m\angle B = 101^\circ$
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7. if m∠ deg = 95, find m∠ def and m∠ feg x = m∠ def = m∠ feg = (diagra…
$x = 40$ $m\angle DEF = 45^\circ$ $m\angle FEG = 40^\circ$
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90+30 6. assuming m∠ deh 180, find m∠ feg m∠ feg = (and there is a diag…
$40^\circ$
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5. if $m\\angle feg = 30$, find $m\\angle deg$ $m\\angle deg = \\underl…
$120^\circ$
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in exercises 7 and 8, find the length of the midsegment of the trapezoi…
7. $14$ 8. $66.5$ 9. $AB = 4$ 10. $AB = 25.9$
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4. name the six different angles in the diagram. ∠ ______ ∠ ______ ∠ __…
$\angle DEF$ $\angle DEG$ $\angle DEH$ $\angle FEG$ $\angle FEH$ $\angle GEH$
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3. find the following lengths. \\(\\overline{ab}\\) ______ \\(\\overlin…
$\overline{AB}=2$ $\overline{BC}=4$ $\overline{AC}=6$
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in exercises 5 and 6, find the measure of each angle in the isosceles t…
Exercise 5: $\angle K = 118^\circ$, $\angle L = 118^\circ$, $\angle J = 62^\circ$, $\angle M = 62^\circ$ Exercise 6: $\angle S = 82^\circ$, $\angle T = 82^\circ$, $\angle R = 98^\…
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1. what does it mean for two points to be collinear? what does it mean …
1. What does it mean for two points to be collinear? Two points are collinear if they lie on the same straight line. What does it mean for two points to be coplanar? Two points ar…
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13) ∠uvw and ∠xyz are complementary angles, ( mangle uvw = (x - 10)^cir…
$x=22$, $m\angle UVW=12^\circ$, $m\angle XYZ=78^\circ$
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0) ∠7 is a supplement of ∠8, and ( mangle7 = 109^circ ). find ( angle8 …
$71^\circ$
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9) ∠5 is a supplement of ∠6, and m∠5 = 78°. find ∠6.
$102^\circ$
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15-18 for independent practice. heck the solutions with your teacher. 8…
$m\angle4 = 44^\circ$
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find the angle measure. (see example 2.) 7) ∠1 is a complement of ∠2, a…
$67^\circ$
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visit www.bigideasmathvideos.com to watch the flipped video instruction…
Linear pairs (any 4 valid pairs): - $\angle 1$ and $\angle 2$ - $\angle 2$ and $\angle 3$ - $\angle 5$ and $\angle 6$ - $\angle 6$ and $\angle 7$ Vertical angle pairs: - $\angle 1…
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1. find the length of the indicated side, to the nearest centimetre. 2.…
Since you haven't specified a particular sub - question from the given set of problems, here's a general approach to solve a triangle - related problem (using the Law of Sines or …
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make a rectangular array of 5 squares. what multiplication sentence des…
\(1\times5 = 5\) (or \(5\times1 = 5\))
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example 2 - finding angle measures a) ∠1 is a complement of ∠2, and ( m…
1. $m\angle5 = 37^\circ$ 2. $m\angle8 = 151^\circ$
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$\\overline{bd}$ bisects $\\angle abc$. find $m\\angle abd$, $m\\angle …
$m\angle ABD = 44^\circ$, $m\angle CBD = 44^\circ$, $m\angle ABC = 88^\circ$
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$\\overrightarrow{qs}$ bisects $\\angle pqr$. use the diagram and the g…
34) $m\angle PQS = 71^\circ$, $m\angle PQR = 142^\circ$ 35) $m\angle PQS = 62^\circ$, $m\angle RQS = 62^\circ$
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qs bisects ∠pqr. use the diagram and the given angle measure to find th…
$m\angle PQS = 71^\circ$, $m\angle PQR = 142^\circ$
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26) m∠xyz = 117°. find m∠xyw and m∠wyz. (6x + 44)° (-10x + 65)°
$m\angle XYW = 32^\circ$, $m\angle WYZ = 85^\circ$
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23) m∠rst = 114°. find m∠rsv.
$42^\circ$
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find rs. rs = work it out not feeling ready yet? these can help.
\( 19 \)
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prove the triangle exterior angle theorem given: δabc prove: ( mangle 4…
By using the Linear Pair Postulate (supplementary angles on a line sum to $180^\circ$) and the Triangle Angle - Sum Theorem (sum of interior angles of a triangle is $180^\circ$), …
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proof of the triangle sum theorem given: △abc and the diagram prove: ( …
By using the Alternate Interior Angles Theorem (for \( \angle 4 \cong \angle 1 \) and \( \angle 5 \cong \angle 3 \)) and the Straight Angle Property (\( m\angle 1 + m\angle 2 + m\…
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find z. right triangle with angles 30°, 60°, 90°, hypotenuse 12 mm, sid…
\(6\sqrt{3}\)
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find k. right triangle with a right angle, one acute angle 45°, the oth…
12
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find d. right triangle with right angle, one angle 30°, one angle 60°, …
\(6\sqrt{3}\)
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find a. right triangle with angles 30°, 60°, 90°; side adjacent to 30° …
\(18\)
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find d. triangle with right angle, 45° angles, side 16√3 mm, side d wri…
\(16\sqrt{6}\)
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find j. right triangle with right angle, one leg 2√2 ft, angle 60°, oth…
$2\sqrt{6}$
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find f. triangle with right angle, 60° angle, 30° angle, side opposite …
\(5\sqrt{2}\)
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find the secant of ∠x. right triangle with right angle at w, leg wx = 4…
$\frac{3\sqrt{7}}{4}$
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find the cotangent of $\\angle p$. simplify your answer and write it as…
\(\frac{8}{15}\)