Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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- 2-1: exit ticket solve for x. 7x + 5 105° x = 10
$x = 10$
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find the measure of ∠1 in the figure, shown to the right. m∠1 = □°
$84$
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in the figure below, m∠1 = 85° and m∠gfj = 141°. find m∠2.
\(56\)
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in the figure below, m∠2 = 60°. find m∠1.
$30^{\circ}$
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select the correct answer from each drop - down menu. complete the sent…
absolute value of the difference
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- 2 - 1: exit ticket alternate exterior angles: same side interior angl…
Alternate Exterior Angles: congruent Same Side Interior Angles: supplementary Vertical Angles: congruent Corresponding Angles: congruent Alternate Interior Angles: congruent Same …
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select the correct answer from each drop - down menu. complete the sent…
distance
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select all the true statements about the angles in the figure. select a…
C. ∠1≅∠3 D. ∠4≅∠8 E. ∠3≅∠6
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given: m∠mxy = m∠kxy what is the conclusion reached by this proof? a. m…
D. \(m\angle JXY = m\angle NXY\)
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- 2-1: exit ticket which of the following is the correct set up for an …
\(180-(x + 112)=105\)
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in the figure below, m∠1 = 37°. find m∠2.
$143^{\circ}$
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which solution finds the value of x in the triangle below? sec 60° = 8/…
$x = 4$
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which solution finds the value of x in the triangle below? sec 60° = 8/…
$x = 4$
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in the figure, m is parallel to n and m∠4 = 118°. find the measures of …
$m\angle1 = 62^{\circ}$, $m\angle2 = 118^{\circ}$, $m\angle3 = 62^{\circ}$, $m\angle5 = 62^{\circ}$, $m\angle6 = 118^{\circ}$, $m\angle7 = 62^{\circ}$, $m\angle8 = 118^{\circ}$
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a napkin is folded into an isosceles triangle, triangle abc, and placed…
30 square centimeters
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law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ how …
No triangles can be formed.
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select the correct answer from each drop - down menu. given: ∠xob≅∠aox …
$m\angle XOB = 90^{\circ}$
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represents the missin dimension x. the area is less than 18 cm² type a …
$0 < x<3$
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triangle klm represents a section of a park set aside for picnic tables…
107 yards
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what is the value of sec θ given the diagram below? (-3, 6) θ -√5 -√5/2…
$-\sqrt{5}$
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congruent? yes no similar? yes no (repeated for four - sets of shapes)
Top - left: Congruent? No, Similar? No Top - right: Congruent? No, Similar? No Bottom - left: Congruent? No, Similar? Yes Bottom - right: Congruent? No, Similar? Yes
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the first figure of the sierpinski triangle has one shaded triangle. th…
\(\sum_{n = 1}^{15}1(3)^{n - 1}\)
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peter and vivian each wrote a proof for the statement: if ∠2 ≅ ∠3, then…
Peter used a direct proof because he used evidence (linear - pair theorem, transitive property of equality) to support the conclusion. Vivian used an indirect proof because the fi…
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find the value of each variable in the figure on the right. x = 72 (sim…
y = 108
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peter and vivian each wrote a proof for the statement: if ∠2 ≅ ∠3, then…
Peter used a direct proof because he used the linear - pair theorem and properties of equality to directly show that if ∠2≅∠3, then ∠1 is supplementary to ∠3. Vivian used a proof …
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which greek mathematician wrote the most definitive text on geometry, o…
C. Euclid
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which pairs of figures are congruent? which pairs are similar?
First pair: Congruent? No, Similar? Yes Second pair: Congruent? Yes, Similar? Yes Third pair: Congruent? No, Similar? Yes Fourth pair: Congruent? No, Similar? Yes
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given: line a and line b intersect prove: ∠1≅∠3 statements reasons 1. l…
D. 2. ∠1 is supplementary to ∠2; 2. linear pair theorem
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which professionals most directly use geometry in their work? a. accoun…
B. astronomers
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identifying similar or congruent shapes on a grid. which pairs of figur…
First pair: Congruent? No, Similar? No Second pair: Congruent? No, Similar? Yes Third pair: Congruent? No, Similar? Yes Fourth pair: Congruent? No, Similar? Yes
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type the correct answer in the box. spell all words correctly. consider…
pyramid
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select the correct answer from each drop - down menu. on this map, oxfo…
Oxford Street is perpendicular to George Street, and Rosewood Street is perpendicular to Oak Street.
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look at this shape: which image shows a translation? a b c
B.
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look at this shape: which image shows a reflection?
B.
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select the correct answer. which statement best defines a circle? a. th…
A. the set of all points in a plane that are the same distance from a given point called the center
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look at this shape: which image shows a rotation?
A.
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a lamppost is 6 feet high and casts an 8 foot shadow. at the same time …
B. 15 ft
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type the correct answer in the box. use numerals instead of words. if n…
$1:1$
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the base of each triangle is 4 cm and the height is 5 cm. what is the s…
40 sq cm
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alana drew a net for a square pyramid. which figure could be the one al…
A.
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select the correct answer form each drop - down menu. given: m∠woz = 90…
The measure of $\angle$WOX equals 90°.
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answer attempt 2 out of 2 a rotation of 90° clockwise about the origin …
A rotation of 90° clockwise about the origin followed by a translation down 4 unit(s).
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which net forms a triangle - based pyramid? a b. c. page 68 / 159
C.
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the figure below is dilated by a factor of 2 centered at the origin. pl…
Plot the points \((-6,-8),(-4,4),(6,6),(6,-2),(2,-2)\) and connect them to form the dilated figure.
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what is the surface area of the square pyramid? 6 sq ft 16 sq ft 24 sq …
16 sq ft
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if a vertical line is dropped from the x - axis to the point (12, - 9) …
$\frac{5}{4}$
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what is the surface area of the right rectangular prism below? 13 in. 6…
C. 308 in.²
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sheila has a box shaped like a right rectangular prism. she wants to co…
A. 300 in.²
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reasoning with parallel and perpendicular lines madison is a developer,…
slope of Moonbeam Drive: $-\frac{4}{5}$ $s(x)=-\frac{4}{5}x + 4$ slope of perpendicular line: $\frac{5}{4}$
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∠1 and ∠2 are complementary given. m∠1 = 36° given. ∠2 and ∠3 are a lin…
D. m∠3 = 126°
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∠1 and ∠2 are complementary given, m∠1 = 36° given, ∠2 and ∠3 are a lin…
# Explanation: ## Step1: Recall linear - pair equation We have the[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]
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on a unit circle, the vertical distance from the x - axis to a point on…
$\pm\frac{2\sqrt{5}}{5}$
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the figure below is dilated by a factor of 1/3 centered at the origin. …
Plot the points $(-\frac{8}{3},2)$, $(2,2)$, $(2,1)$, $(2,-1)$, $(0,-2)$ and connect them in order to get the dilated image.
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what is the surface area of th
$712$ $cm^2$
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in the figure, m is parallel to n and m∠4 = 123°. find the measures of …
$m\angle1 = 57^{\circ}$, $m\angle2 = 123^{\circ}$, $m\angle3 = 57^{\circ}$ (assuming the standard naming of angles formed by two parallel lines and a transversal)
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drag each label to the correct location on the chart. given: ∠1≅∠2 prov…
Drag $\angle1\cong\angle3$ to the box above $\angle2\cong\angle3$ (because of vertical - angles theorem). Drag $\angle2\cong\angle4$ to the box below $\angle2\cong\angle3$ (becaus…
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statements 1. ∠boc and ∠cod are complementary angles; bo intersects ad …
The missing step is between step 2 and step 3, and it should be \(m\angle BOC + m\angle COD=m\angle BOD\) with the reason "angle - addition postulate".
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henry is asked to find the exact value of cos(10π/3). his steps are sho…
Henry made an error in calculating the reference angle (step 2) and also in determining the sign of the cosine value (step 4). The correct reference angle for \(\frac{4\pi}{3}\) i…
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the figure below is dilated by a factor of $\frac{1}{3}$ centered at th…
Plot the points $V'(0, - 2)$, $W'(2,-1)$, $X'(2,1)$, $Y'(\frac{4}{3},2)$, $Z'(-3,2)$ and connect them.
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select the correct answer from each drop - down menu. given: ∠boc and ∠…
The proof is completed as shown in the steps above to prove $\angle AOB\cong\angle BOD$.
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point q is located at (6, - 1) on the coordinate plane. point q is refl…
$(-6,1)$
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point e is located at (3, -5) on the coordinate plane. point e is refle…
$(-3,5)$
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using the graph, determine the coordinates of the zeros of the parabola.
The zeros of the parabola are the x - intercepts. From the graph, the x - intercepts are at \(x = 4\) and \(x = 8\). So the coordinates of the zeros are \((4,0)\) and \((8,0)\).
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find the measure of ∠j, the smallest angle in a triangle with sides mea…
$34^{\circ}$
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a spinner for a board game consists of a cardboard circle with two plas…
7.7 square centimeters
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what is the measure of ∠c to the nearest whole degree? 70° 77° 80° 85° …
\(77^{\circ}\)
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what is the length of line segment rs? use the law of sines to find the…
2.4 units
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which statement describes the relationship between the intercepts of fu…
D. The x - intercept of b is greater than the x - intercept of a.
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determine if triangle pqr and triangle stu are or are not similar, and,…
The triangles $PQR$ and $STU$ are similar by the AA (angle - angle) similarity criterion.
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determine if triangle klm and triangle nop are or are not similar, and,…
The triangles $KLM$ and $NOP$ are not similar because only one pair of angles is equal and the other pair of corresponding angles are not equal.
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which equation correctly uses the law of cosines to solve for y? o 9² =…
$y^{2}=9^{2}+19^{2}-2(9)(19)\cos(41^{\circ})$ (the fourth option)
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find the measure of ∠q, the smallest angle in a triangle whose sides ha…
$41^{\circ}$
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6. what is the measure of angle x? 75° 36° x = ____
\(111^{\circ}\)
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a kite is made up of two isosceles triangles, kit and ket, with the len…
48 square inches
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triangle abc is a sketch of a triangular flower bed that has an area of…
40 feet
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3. triangle abc will be rotated 90 degrees clockwise about the origin. …
$(5,2)$
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law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ tria…
B. $30^{\circ}$
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law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ in $…
D. $45^{\circ}$ and $135^{\circ}$
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if △cab is dilated and rotated, it maps on to △def. what is the measure…
None of the above (since the correct answer \(31^{\circ}\) is not in the options A. \(26^{\circ}\), B. \(28.5^{\circ}\))
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the law of cosines for △rst can be set up as 5² = 7² + 3² - 2(7)(3)cos(…
D. $s = 5$ and $t = 3$
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what is the measure of ∠n to the nearest whole degree? 35° 45° 55° 65° …
$55^{\circ}$
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5. lines v and w are parallel lines cut by a transversal. 39° (6x + 3)°…
6
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two teams are pulling a heavy chest, located at point x. the teams are …
$\frac{\sin(A)}{2.4}=\frac{\sin(110^{\circ})}{4.6}$ (corresponding to the first option in the multiple - choice list)
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which measures are accurate regarding triangle jkl? select two options.…
$k\approx3.2$ units, $KL\approx3.2$ units
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what is the area of triangle dfg? round to the nearest whole square uni…
27 square units
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what is the area of triangle pqr? round to the nearest tenth of a squar…
70.5 square units
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which fact from the tinker v. des moines court decision best supports t…
A. That they are educating the young for citizenship is reason for scrupulous protection of Constitutional freedoms of the individual, if we are not to strangle the free mind at i…
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are the triangles congruent? why or why not? yes, ∠a≅∠d and ab≅de. yes,…
No, $\angle C$ is not congruent to any angle in $\triangle DEF$.
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given that d is the midpoint of $overline{ab}$ and b is the midpoint of…
B. $AC = 4DB$
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true converses? 211° 67° (x + 40)°
\(x = 42\)
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the ratio of the circumferences of two circles is 2:3. if the large cir…
B. 26 cm
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the triangles are congruent by the sss congruence theorem. which rigid …
rotation, then translation
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3. solve the inequality, write the solution in set notation, and graph …
For \(-5(4x - 1)>-55\): Solution Set: \(\{x|x < 3\}\) Graph: Open - circle at \(3\), shade to the left. For \(3\leqslant4x - 9\leqslant11\): Solution Set: \(\{x|3\leqslant x\leqsl…
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how do the areas of triangle abc and def compare? the area of △abc is 1…
The area of △ABC is equal to the area of △DEF.
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if tu = 6 units, what must be true? su + ut = rt rt + tu = rs rs + su =…
SU + UT = RT
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point s lies between points r and t on $overline{rt}$. if rt is 10 cent…
6 centimeters
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how does the area of triangle rst compare to the area of triangle lmn? …
The area of $\triangle RST$ is 2 square units greater than the area of $\triangle LMN$.
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what is true about △abc? select three options. ab ⊥ ac. the triangle is…
A. $\overline{AB}\perp\overline{AC}$ B. The triangle is a right triangle. C. The triangle is an isosceles triangle.
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for each list, circle the one that is not equivalent to the rest. 9.) -…
9. $\frac{-a}{-b}$ 10. $-\frac{x}{y}$ 11. $-(\frac{3}{-7})$ 12. $-\frac{1}{x}$
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3. solve the inequality, write the solution in set notation, and graph …
For $-5(4x - 1)>-55$: Solution Set: $\{x|x < 3\}$ Graph: An open - circle at 3 on the number line and a line extending to the left. For $3\leq4x - 9\leq11$: Solution Set: $\{x|3\l…