Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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what is the measure of $\\angle xyz$?\ \ a. $75^\\circ$\ b. $108^\\circ…
D. $54^\circ$
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look at the above painting. which of the following elements of the pain…
c. The height of the man and woman as compared to all the other people.
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what is the measure of (overarc{ac})? a. (150^circ) b. (120^circ) c. (3…
A. $150^\circ$
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question 8 of 10 the measure of an angle formed by ________ is half the…
B. intersecting chords
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practice determining the measures of line segments and angles. what is …
point N
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question 7 of 10 what is the measure of ∠xyz? a. 36° b. 72° c. 55° d. 1…
A. $36^\circ$
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what is the measure of $\\angle xyz$? a. $64^\\circ$ b. $108^\\circ$ c.…
D. $72^\circ$
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question 5 of 10 intersecting chords form a pair of congruent, vertical…
A. True
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what is the measure of a. 128° b. 38° c. 142° d. 52°
B. \(38^\circ\)
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7. in △abc shown below, l is the midpoint of (overline{bc}), m is the m…
35
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in the diagram, ∠jkm is a straight angle. which statements about the di…
- \(\overrightarrow{KQ}\) is an angle bisector: True - \(\angle LKQ\) is bisected: True - \(m\angle JKL = 45^{\circ}\): False - \(m\angle MKQ + m\angle PKQ=m\angle PKM\): True (co…
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question 3 of 10 what is the measure of \\(\\angle abc\\)? a. \\(126^\\…
B. $63^\circ$
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which expression gives the measure of $\\angle abc$? a. $110^\\circ - 2…
B. $\frac{1}{2}(110^{\circ} - 20^{\circ})$
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6.5.4 quiz: intersecting chord theorem question 1 of 10 what is the mea…
D. $29^\circ$
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what is the volume of the cube? 7 cm 21 cm³ 49 cm³ 147 cm³ 343 cm³
D. \( 343 \, \text{cm}^3 \)
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question 10 of 10 what is the measure of $\\angle abc$ a. $59^\\circ$ b…
A. $59^\circ$
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question 9 of 10 the measure of an inscribed angle in a circle is _____…
B. half
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find each measure. 1. rs 2. xz list the angles and sides of each triang…
1. $RS = 9$ 2. $XZ = 34$ 3. Sides (smallest to largest): $RT, TS, SR$; Angles (smallest to largest): $\angle S, \angle R, \angle T$ 4. Angles (smallest to largest): $\angle A, \an…
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question 6 of 10 what is the measure of ∠xyz? a. 68° b. 34° c. 136° d. …
B. $34^\circ$
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question 5 of 10 an inscribed angle is an angle formed by two chords th…
A. True
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question 4 of 10 what is the measure of \\(\\angle xyz\\)? 148° a. 148°…
C. $74^\circ$
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question 3 of 10 what is the measure of overline{xz}? a. 36° b. 72° c. …
D. $144^\circ$
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part 2 find the measure of each numbered angle. 1. $\\angle 1$ 2. $\\an…
1. $m\angle 1 = 70^\circ$ 2. $m\angle 2 = 110^\circ$ 3. $m\angle 3 = 42^\circ$ 4. $x = 104^\circ$ 5. $m\angle 1 = 72^\circ$, $m\angle 2 = 39^\circ$
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question 2 of 10 what is the measure of (overarc{xyz})? a. (300^circ) b…
B. $240^\circ$
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question 1 of 10 what is the measure of (overarc{xyz})? a. (196^circ) b…
A. $196^\circ$
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5. reinforce you plan to walk from home along the indicated route. you …
a. Missing coordinates: - Top right point (between School and Library): $(6,2)$ - Bottom middle point (between Park and Home): $(0,-3)$ b. Total route distance: $36$ c. Enclosed a…
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3. brandon sketched two signs on a coordinate plane. each gridline repr…
- The two signs require the same amount of material. --- ### Problem 4
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applying the angle addition postulate in the diagram below, ∠dab and ∠d…
s: - \( m\angle DAB = \boldsymbol{80^\circ} \) - \( m\angle BAC = \boldsymbol{105^\circ} \)
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which of the following countries was not part of the heavily industrial…
B. the United Kingdom
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question 10 of 10 if chord \\(\\overline{ab}\\) is congruent to chord \…
D. $43^\circ$
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given ⊙o below, the arcs \\(\\overarc{ab}\\) and \\(\\overarc{cd}\\) mu…
B. False
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given ⊙o below, if (overarc{gh}) and (overarc{jk}) are congruent, what …
C. $68^\circ$
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given ⊙o below, if \\(\\overline{ab}\\) and \\(\\overline{bc}\\) are co…
A. 12.5 units
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two chords in the same circle are congruent if and only if the associat…
A. True
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question 5 of 10 given \\( \\odot o \\) below, the arcs \\( \\overarc{w…
A. True
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question 4 of 10 given ⊙o below, if (widehat{gh}) and (widehat{hj}) are…
A. $150^\circ$
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two arcs of a circle are congruent if and only if their associated radi…
B. False
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question 2 of 10 two arcs are congruent if they have the same measure a…
B. congruent circles D. the same circle
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question 1 of 10 given \\(\\odot o\\) below, if \\(\\overarc{ab}\\) and…
B. 5 units
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find the value of x from the previous question. the ratio of the measur…
$20^\circ$
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a central angle of a circle is an angle whose vertex is anywhere inside…
B. False
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a minor arc will have a measure that is ______. a. equal to 180° b. les…
B. less than $180^\circ$
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the ______ of a central angle are two radii of the circle. a. measurea …
C. sides
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given ⊙q below, is widehat{yor} a minor arc, a major arc, or a semicirc…
C. Major arc
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an arc that measures 180° is called a ______. a. semicircle b. major ar…
A. semicircle
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question 5 of 10 given \\(\\odot o\\) below, is \\(\\overarc{pq}\\) a m…
A. Semicircle
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part 1 find the sum of the measures of the interior angles of each conv…
1. $1440^\circ$ 2. $2340^\circ$ 3. $65^\circ$ 4. $18$ 5. $12$ 6. $115^\circ$ 7. $33^\circ$ 8. $13^\circ$ 9. $64$ feet 10. $180^\circ$ 11. $6$
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this is level 1; reflect a shape in a given line. click on coordinates …
For the green shape: The reflected shape will be a mirror image of the green shape across the \(y\) - axis, with all \(x\) - coordinates of the vertices negated (while \(y\) - coo…
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an arc that lies outside of a central angle is called a ______. a. semi…
B. major arc
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what is the measure of $overarc{efg}$ in $odot o$ below? a. $300^circ$ …
A. $300^\circ$
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question 1 of 10 what is the measure of \\(\\overarc{ab}\\) in \\(\\odo…
B. $260^\circ$
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question 10 of 10 the blue segment below is a radius of ⊙o. what is the…
C. 25.4 units
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question 9 of 10 which of the following segments is a diameter of ⊙o? a…
A. $\overline{UV}$
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the blue segment below is a diameter of \\(\\odot o\\). what is the len…
A. 2.95 units
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question 7 of 10 what is another name for a chord that passes through t…
A. Diameter
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question 6 of 10 the chord (overline{bc}) is a diameter of (odot o). a.…
A. True
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leveled practice in 7 and 8, find the missing 7. $\\square^2 + 12\\squa…
(for the assumed case): If the right - triangle has legs \(4x + 4\) and \(3x\), when \(x = 2\), the hypotenuse \(c=\sqrt{(4x + 4)^{2}+(3x)^{2}}\). Substituting \(x = 2\): \(4x+4=1…
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practice & problem solving leveled practice in 7 and 8, find the missin…
The length of the hypotenuse is \(\boldsymbol{15}\) units. ### Problem 8
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question 4 of 10 the chord (overline{xy}) is a diameter of (odot o). a.…
A. True
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question 3 of 10 the blue segment below is a radius of \\(\\odot o\\). …
D. 18.6 units
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line 1 passes through (5, 2) and (5, 8) line 2 passes through (- 1, 4) …
Line 1 is a vertical line $x=5$, Line 2 is a horizontal line $y=4$, so the two lines are perpendicular to each other.
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question 1 of 10 which best describes the diameter of a circle? a. the …
C. The distance across the middle of the circle
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if the blue radius below is perpendicular to the green chord and the se…
B. 15.2 units
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if a radius of a circle is perpendicular to a chord, then it ______ tha…
C. bisects
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question 8 of 10 true or false? the blue radius is perpendicular to the…
B. False
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true or false? if a radius of a circle is perpendicular to a chord, the…
A. True
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question 6 of 10 true or false? in ⊙ o, radius (overline{op}) intersect…
A. True
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exercises is it possible to form a triangle with the given side lengths…
1. Yes, a triangle can be formed. 2. No, because $6+9=15$, which does not satisfy the triangle inequality (sum of two sides must be greater than the third side). 3. Yes, a triangl…
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if the blue radius below is perpendicular to the chord \\(\\overline{ac…
B. 7 units
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question 3 of 10 if the blue radius below is perpendicular to the green…
D. 17 units
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true or false? the blue radius is perpendicular to the green chord. a. …
A. True
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true or false? the segment \\(\\overline{ab}\\) is congruent to the seg…
B. False
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what is the length of the blue segment in \\(\\odot l\\) below? a. 7.9 …
C. 7.74 units
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question 9 of 10 fill in the blank. two chords that are the same distan…
B. congruent
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question 8 of 10 fill in the blank. given \\( \\odot o \\) below, you c…
D. $\overline{OE}$
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question 6 of 10 what is the length of chord (overline{vi}) in (odot c)…
D. 18.6 units
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question 5 of 10 fill in the blank. if two chords of a given circle are…
C. be equidistant from the center of the circle
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fill in the blank. given ⊙e below, you can conclude that (overarc{cd}) …
C. $\overline{AB}$
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what is the length of chord $overline{st}$ in $odot p$ below? a. 3.5 un…
C. 7 units
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determining trigonometric ratios of similar triangles consider δabc ~ δ…
1. $\tan(A) = \frac{3}{4}$ 2. $\tan(X) = \frac{3}{4}$ 3. The two tangent ratios are equal.
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question 1 of 10 a chord of a circle is a line segment connecting any p…
B. False
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read 7.3 inequalities in one triangle (textbook pgs. 426 - 429) angle -…
1. Angles: $\boldsymbol{\angle T < \angle R < \angle S}$; Sides: $\boldsymbol{\overline{SR} < \overline{TS} < \overline{TR}}$ 2. Angles: $\boldsymbol{\angle T < \angle R < \angle …
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question 10 of 10 a radius is a segment that connects any point on the …
A. True
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question 9 of 10 a circle is the collection of points in a plane that a…
B. False
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all the radii of a circle have different lengths. a. true b. false
B. False
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what is the center of the circle shown below? a. a b. $overline{ab}$ c.…
C. B
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question 6 of 10 the distance around a circle is called the ______. a. …
A. circumference
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analyzing cofunctions consider △lmn. m∠l + m∠m = sin(l) = sin(m) =
$m\angle L + m\angle M = 90$ $\sin(L) = \cos(M)$ $\sin(M) = \cos(L)$
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which is the best estimate of the circumference of this circle? a. 18 u…
A. 18 units
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consider △xyz what are the ratios of sine, cosine, and tangent for angl…
$\sin(Y)=\frac{XZ}{XY};\cos(Y)=\frac{YZ}{XY};\tan(Y)=\frac{XZ}{YZ}$ (the third option)
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b e 2√96 4√10 18 12 d 4 f a 8 c m∠a m∠d a. < b. > c. = d. cannot be det…
B. >
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what is the largest integer value of mo for which rhombus mnop will hav…
C. 17
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is the triangle with the given dimensions a right triangle? if so, whic…
D. No, it is not a right triangle.
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create similar right triangles by changing the scale factor of the righ…
1. When scale factor is 1: $\boldsymbol{\frac{1}{2}}$ 2. When scale factor is 3: $\boldsymbol{\frac{1}{2}}$ 3. For any 30° angle: $\boldsymbol{\frac{1}{2}}$
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determine if the segment lengths form a triangle. if so, would the tria…
C. Yes, the segments would form a right triangle.
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the sides of a triangle have lengths of x, x + 4, and 20. if the longes…
(longest $c$), $a^2 + b^2 < c^2$ ## Step2: Substitute given sides $x^2 + (x+4)^2 < 20^2$ ## Step3: Expand and simplify inequality $x^2 + x^2 +8x +16 < 400$ $2x^2 +8x - 384 < 0$ $x…
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can a triangle have an angle that measures 179°? if so, what type of tr…
of angles in a triangle is $180^\circ$. ## Step2: Calculate remaining angle sum $180^\circ - 179^\circ = 1^\circ$, so the other two angles add to $1^\circ$. ## Step3: Classify by …
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find an integer, x, such that 2, 4, and x represent the lengths of the …
B. 3
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(a) find the slope of the line through (7,2) and (48, -2) (b) based on …
A. The slope of the line is \(\boldsymbol{-\frac{4}{41}}\) ### Part (b)
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labeling sides of right triangles complete the table to show the name o…
| | $a$ | $b$ | $c$ | |----------|--------------------|--------------------|--------------| | $\angle A$ | Opposite Side | Adjacent Side | Hypotenuse | | $\angle B$ | Adjacent Sid…