Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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the diameter of a circle is 151 m. find the circumference to the neares…
$474$ m
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what is the area of this figure? square inches
180
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points b and d are the endpoints of a diameter of the circle. how are t…
Because \(BD\) is a diameter, then \(\overparen{DAB}\) is a semi - circle. So, the sum of \(m\overparen{AB}\) and \(m\overparen{AD}\) will be \(180^{\circ}\).
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question the diameter of a circle is 151 m. find the circumference to t…
$474$ m
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how does the measure of ∠abd compare to the measure of ∠acd? explain yo…
The measures of the angles are equal because the intercepted arc of both angles is the same.
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18. in order to construct a bridge across a lake, an engineer wishes to…
18. $494.23$ m 19. $42^{\circ}$ 20. $6.43$ ft 21. $7421.23$ m
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question 8 (1 point) in the figure below, angle 6 and angle 8 are an ex…
c) corresponding angles
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a circular garden is divided into three sections with different - color…
$169.5^{\circ}$
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given: ∠dba is inscribed in circle c, where c is outside ∠dba. prove: m…
The proof that \(m\angle DBA = \frac{1}{2}m\overset{\frown}{DA}\) is based on the properties of inscribed angles and central angles in a circle, the construction of isosceles tria…
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look at this diagram: which diagram shows quadrilateral efgh rotated 30…
The given diagram shows quadrilateral EFGH rotated 30° counterclockwise about F.
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question 5 (1 point) in the figure below, angle 6 and angle 3 are an ex…
A. alternate interior angles
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persevere a point in the second quadrant with coordinates (-a, b) is re…
$(-b,a)$
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which pair of angles in the diagram are alternate interior angles? a ∠1…
Question 13: D. ∠2 and ∠3 Question 14: G. 4
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michael stands outside of a circular opening. he points a flashlight at…
D. 100°
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part b compare the measures of the central angles to the measure of the…
None of the given options are correct as the measure of the angle between the secants is half of the positive difference of the measures of the central angles corresponding to the…
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draw central angles that intercept the same arcs as the secants. which …
The second option (the one with angles having vertices at the center of the circle)
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19. rectangles the formula p = 2ℓ + 2w represents the perimeter of a re…
a. $\ell=\frac{P - 2w}{2}$ b. 14 meters
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two chords intersect inside a circle, forming vertical angles. the inte…
\(44^{\circ}\)
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find the value of x. recall that m∠bcd = 1/2 (mad - mbd). enter the cor…
$35$
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figure is shown. y 10 9 8 7 6 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 com…
$60^{\circ}$; $20^{\circ}$
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match each angle pair to its proper categorization: column a 1. angle 2…
1. a. Corresponding Angles 2. c. Alternate Exterior Angles 3. No match among given options 4. d. Alternate Interior Angles
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an incomplete proof is shown. given: ∠cpn and ∠plh are supplementary. p…
2. $m\angle CPN + m\angle PLH = 180^{\circ}$ 5. $m\angle LFK+m\angle PLH = 180^{\circ}$ 6. $\angle LFK$ and $\angle PLH$ are supplementary 7. If two same - side interior angles ar…
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two parallel lines, m and n, are cut by the transversal d as shown. sup…
We see that ∠2 and ∠3 are alternate interior angles. And since the lines m and n are parallel, ∠2 and ∠3 are congruent. So, \(m\angle3 = 135^{\circ}\). We see that ∠1 and ∠2 are a…
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al||dh, where ph is a transversal. given m∠dhj=(4x - 9)° and m∠ajh = 10…
The measure of $\angle DHJ$ is $45^{\circ}$ and the measure of $\angle AJH$ is $135^{\circ}$. They are supplementary because they are same - side interior angles.
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question 8 (1 point) in the figure below, angle 6 and angle 8 are an ex…
a) alternate interior angles
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the figure below is a net for a right rectangular prism. its surface ar…
The area of each missing face is 24 ft² The length of each missing edge is 3 ft
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given $m\\angle rhw=(x + 20)^{circ}$ and $m\\angle mgf=(9x + 5)^{circ}$…
The $m\angle WHT$ is $(x + 20)^{\circ}$ (or $21.875^{\circ}$ when $x=\frac{15}{8}$) because it is congruent to $\angle RHW$.
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question 5 (1 point) in the figure below, angle 6 and angle 3 are an ex…
A. alternate interior angles
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which two quotations best describe johnsons achievements? a. \johnson d…
C. "It was the first time a woman in the Flight Research Division had received credit as an author of a research report." (Paragraph 3) F. "She also worked on the Space Shuttle an…
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in the figure, $overleftrightarrow{hl}paralleloverleftrightarrow{yr}$, …
$m\angle BFX = 37^{\circ}$, $m\angle LXW = 143^{\circ}$, $m\angle WXL = 37^{\circ}$, $m\angle YBM = 143^{\circ}$
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a diagram is shown where $overleftrightarrow{rg}paralleloverleftrightar…
The value of $x$ is $54$. The measure of $\angle NKB$ is $126^{\circ}$. The measure of $\angle HTD$ is $56^{\circ}$.
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classify the angle pair ∠5 and ∠8. f vertical angles g alternate interi…
Question 16: F. Vertical angles Question 17: D. ∠2 and ∠7
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which type of lines are not represented in the diagram? (a) parallel li…
C. Skew lines F. Vertical angles
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question 13 (2 points) which pair of angles in the diagram are alternat…
Question 13: D. $\angle2$ and $\angle3$ Question 14: G. 4
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complete the proof. given: ∠gnd and ∠pdk are supplementary. prove: line…
1. Reason for $\angle GND\cong\angle BNR$: Vertical Angles Theorem 2. Reason for $\angle BNR$ and $\angle PDK$ are supplementary: Definition of Supplementary Angles 3. Reason for …
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write an expression that represents the perimeter of the figure below. …
$4d + 8g$
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which quotation best supports the idea that people trusted johnson? a. …
C. "If she says they're good,' Johnson remembers the astronaut saying, 'then I'm ready to go.'" (Paragraph 4)
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wy || vp, where rz is a transversal. given m∠rtv = 141° and m∠wxz = 39°…
The $m\angle YXZ = 141^{\circ}$ because $\angle RTV$ and $\angle YXZ$ are corresponding angles.
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4. a regular pyramid has a square base. the perimeter of the base is 48…
720 cubic inches
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write an expression that represents the perimeter of the figure below. …
$2d + 2e+8f$
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the perimeter of the figure below is 69.6 ft. find the length of the mi…
$10.7$
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find the perimeter of the figure below, in centimeters. (note: diagram …
$166.4$
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question: find the perimeter of the figure below, in centimeters. (note…
216.6 cm
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the perimeter of the figure below is 151.3 ft. find the length of the m…
$9.6$ ft
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for the purpose of purchasing new baseboard and carpet, complete parts …
a. (No values are given to calculate actual area and perimeter, so we can't fill in the blanks with numbers) b. B. The baseboard has to do with perimeter and the carpet has to do …
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8. find m ∠ bfh type a response m||n
\(68\)
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7. find m ∠ fcd type a response m||n
$43$
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question: the square below is dilated by a scale factor of 4. find the …
Perimeter of given square: 48 units Area of given square: 144 units² Perimeter of dilated square: 192 units Area of dilated square: 2304 units²
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by decreasing each dimension by 1 unit, the area of a rectangle decreas…
$28$
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6. find m ∠ abd. type a response
\(27^{\circ}\)
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question 12 (4 points) match each angle pair with the correct transvers…
1. d. Transversal: line p & Same - Side Interior Angles 2. a. Transversal: line q & Alternate Interior Angles 3. c. Transversal: line $\ell$ & Alternate Exterior Angles 4. b. Tran…
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question 11 (4 points) match each angle pair to its proper categorizati…
1. c. Corresponding Angles 2. a. Alternate Exterior Angles 3. b. Alternate Interior Angles 4. d. Same - Side Interior Angles
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question 10 (4 points) match the following column a 1. one pair of para…
1. d. segment AB and segment CF 2. a. segment AB and segment DE 3. b. segment BD and segment DF 4. c. plane ABC and plane DEF
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question the right triangle below is dilated by a scale factor of 3. fi…
Perimeter of given right triangle: 24 units Area of given right triangle: 24 units² Perimeter of dilated right triangle: 72 units Area of dilated right triangle: 216 units²
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write the coordinates of the y - intercept.
(0, - 250)
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question 9 (4 points) identify the transversal and classify each angle …
1. a. Transversal: line n & Corresponding Angles 2. c. Transversal: line m & Alternate Exterior Angles 3. d. Transversal: line n & Alternate Interior Angles 4. b. Transversal: lin…
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question 8 (1 point) in the figure below, angle 6 and angle 8 are an ex…
c) corresponding angles
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question 7 (1 point) in the figure below, angle 2 and angle 4 are an ex…
a) alternate interior angles
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given: $overline{ab}congoverline{cd}$ prove: $overline{ac}congoverline{…
3. Segment - addition postulate; 4. Substitution Property of Equality
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question 6 (1 point) in the figure below, angle 2 and angle 3 are an ex…
d) same - side interior/consecutive interior angles
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10. consider the table below: x y 2 10 5 6 8 2 11 -2 what is the change…
\(\Delta Y=-4\) \(\Delta X = 3\) \(\frac{\Delta Y}{\Delta X}=-\frac{4}{3}\)
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consider the figure. use the diagram to verify formulas. part a find th…
$m\angle RPQ=180-\frac{1}{2}m\overparen{RQ}$
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step 1 step 2 step 3 how many more line segments will be needed to be a…
16
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consider the figure. use the diagram to verify formulas. part a find th…
\(m\angle{RPQ}=180 - m\widehat{RQ}\)
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find m\\(\\overparen{km}\\). drag the correct answers into the boxes. h…
$139^{\circ}$
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find m\\(\\overparen{km}\\). drag the correct answers into the boxes. s…
$m\overparen{KM}=139^{\circ}$
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2. a dog is tied with a rope to a stake in the ground. the length of th…
(3) $25\pi$
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3. explain why your argument will work for any triangle: that is, expla…
The sum of the angle measures in any triangle is $180^{\circ}$ because by constructing a parallel line to one side of the triangle through the opposite vertex, we can use the prop…
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1 use angle relationships to complete the top equation. then, solve the…
The completed equation is \(14x + 4x=180^{\circ}\), \(x = 10^{\circ}\), \(14x = 140^{\circ}\), \(4x = 40^{\circ}\)
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3. a white line, parallel to your lane, on the right, indicates: a. a l…
3. D. The edge of the vehicular portion of a roadway, and may not be crossed 4. D. When it is a right angle (90 degrees)
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name the ordered pair for each point on the city map at the right. 20. …
20. $(0,0)$ 21. $(-6,-4)$ 22. $(6,2)$ 23. $(-5,5)$
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find m\\(\\widehat{ac}\\). show your work. drag the expressions into th…
$85^{\circ}$
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line y is parallel to line z. find the measures of the angles q, r, and…
$m\angle Q = 140^{\circ}$ $m\angle R = 40^{\circ}$ $m\angle S = 140^{\circ}$
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name: ak lam date: period: problem set #2 show all work. 1. the area of…
$120^{\circ}$
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graph and label each point on the coordinate plane. 11. n(-1,3) 12. v(2…
Points N(-1,3), V(2,-4), F(-6,2), K(-1,5), A(5,-3), C(4,0), M(-5,0), I(-3,-3), D(0,-5) are plotted and labeled on the coordinate - plane according to the above steps.
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4. is the measure of angle eab equal to the measure of any angle in tri…
1. $m\angle DBA + b+m\angle CBE = 180^{\circ}$ because the sum of angles on a straight line is $180^{\circ}$. 2. Since $\angle DBA=a^{\circ}$ and $\angle CBE = c^{\circ}$ (alterna…
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find m\\(stackrel{\frown}{ac}). show your work. drag the expressions in…
# Explanation: ## Step1: Recall the inscribed - angle theorem The measure of an inscribed angle is half the measure of its intercepted arc. The measure of an angle formed by two c…
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find m∠ejf. drag the expressions into the boxes to correctly complete t…
$52^{\circ}$
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drag the expressions into the boxes to correctly complete the solution.…
$32^{\circ}$
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6. in the diagram, lines $overline{pr}$ and $overline{st}$ intersect at…
(a) $x = 22$ (b) $m\angle RQT=150^{\circ}$ (c) $m\angle PQT=30^{\circ}$
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find the distance between the point and the line. round your answer to …
1. Approximately \(4.9\) 2. Approximately \(3.1\)
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5. angles j and k are supplementary. the measure of ∠k is nine times th…
The measure of $\angle J$ is $18^{\circ}$ and the measure of $\angle K$ is $162^{\circ}$.
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4. in the diagram below, ∠abc is a right angle. if m∠abd = 13x and m∠db…
$38$
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3. in the diagram shown below, lines $overline{zw}$, $overline{ux}$ and…
$m\angle VYZ = 90^{\circ}$, $m\angle ZYU=36^{\circ}$, $m\angle XYZ = 54^{\circ}$, $m\angle XYW = 144^{\circ}$, $m\angle UYW = 144^{\circ}$
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2. in the diagrams shown below, fill in the measure of each missing ang…
(a) 67° (b) 134° (c) 53°
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practice - angle pairs n - gen math® 8 1. angle e and angle f are compl…
\(66^{\circ}\)
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14. what is the distance between the points (3,5) and (8,10)? 7.07 6.40…
7.07
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draw a picture that shows 3 + (2 x 19).
Draw 2 rows of 19 circles each and then 3 additional circles.
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use what you know about the interior angle measures of triangles to com…
Angle \(K = 90^{\circ}\) Angle \(L = 62^{\circ}\)
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use what you know about the interior angle measures of triangles to com…
Angle $P = 100^{\circ}$, Angle $R = 8^{\circ}$ (There are multiple possible answers as long as one angle is obtuse and the sum of the two non - given angles is 108°)
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unit #2 - warmup problem #4: in the diagram below, line segment $overli…
Point I is the mid - point of $\overline{HJ}$ because $\overline{HI}=\overline{IJ}=100$ when $x = 7$.
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unit #2 - warmup problem #3: in the diagram, segments $overline{st}$ an…
$x = 20$ $m\angle SRP = 40^{\circ}$ $m\angle PRT = 140^{\circ}$ $m\angle QRT = 40^{\circ}$ $m\angle SRQ = 140^{\circ}$
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at a certain time of day, a tree that is x meters tall casts a shadow t…
96 meters
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find the slope of the line in the figure. select the correct choice bel…
A. The slope of the line is $-\frac{1}{2}$
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match the definitions to the mathematical terms they describe. all copl…
"all coplanar points equidistant from a given point" -> circle "piece of a line with two endpoints" -> line segment "two rays with a common endpoint" -> angle "piece of a line wit…
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figure c is the result of a transformation on figure b. which transform…
A. A rotation 90° clockwise about the origin
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figure h is the result of a transformation on figure g. which transform…
A rotation 90° counterclockwise about the origin
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figure b is the result of a transformation on figure a. which transform…
A. A reflection over the y - axis
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figure t is the result of a transformation on figure s. which transform…
A reflection over the \(y\) - axis
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△def ≅ △stu. what is m∠u?
$42$