幾何
三角形、圓、解析幾何與證明題。
-
point a is the incenter of δdef. what is the length of na? options: 2 u…
9 units
-
point y is the circumcenter of δdef. find fy. diagram of δdef with circ…
22
-
point a is the incenter of triangle def. which must be true? select thr…
B. Point A is the center of the circle that passes through points X, Y, and Z C. \(\overline{ZA} \cong \overline{YA}\) E. \(\overline{AX} \cong \overline{AY}\)
-
which is the only center point that lies on the edge of a triangle? ○ t…
C. the circumcenter of a right triangle
-
point a is the incenter of δdef. what is the value of n? 7, 11, 14, 15 …
11
-
three friends want to meet at a place that is the same distance from ea…
Find the midpoint of the segments which connect their houses.
-
an orthocenter is the intersection of three ○ angle bisectors in a tria…
B. altitudes in a triangle.
-
in the diagram, gb = 2x + 3.. what is gb? ○ 5 units ○ 10 units ○ 15 uni…
15 units
-
in which type of triangle is the orthocenter on the perimeter of the tr…
a right triangle
-
in triangle nlm, point s is the centroid, qs = (3x − 5) cm, and ns = (4…
20 cm
-
point g is the centroid of triangle abc. the length of segment cg is 6 …
18 units
-
in triangle trs, tz = (3x) inches and wz = (2x - 3) inches. what is wz?…
9 inches
-
a centroid is the intersection of three ○ altitudes in a triangle. ○ pe…
D. medians in a triangle.
-
in triangle nql, point s is the centroid, ns = (x + 10) feet, and sr = …
7 feet
-
point g is the centroid of triangle abc. ag = (5x + 4) units and gf = (…
51 units
-
3 what is the volume of a box that has length of 24 cm, a width of 11 c…
The volume of the box is \( 3960 \, \text{cubic centimeters} \) (or \( 3960 \, \text{cm}^3 \)). ### Problem 4: Miles Driven in a Year
-
triangle abc is shown below. what is the length of line segment ac? 7 9…
14
-
angle m has a measure of 47°. what is the measure of angle pnl? 43° 47°…
\( 43^\circ \) (corresponding to the option with \( 43^\circ \))
-
practice 21.2 volume of pyramids find the volume of each pyramid. round…
The volume of the hexagonal pyramid is \( 75 \, \text{cubic feet} \) (or \( 75 \, \text{ft}^3 \)).
-
triangle sqt is isosceles. the measure of angle stq is 48°. what is the…
\( 24^\circ \) (corresponding to the option with \( 24^\circ \))
-
the vertex angle of an isosceles triangle measures 40°. what is the mea…
\(70^\circ\) (corresponding to the option with \(70^\circ\))
-
triangle xyz is isosceles. the measure of the vertex angle, y, is twice…
A. Angle Y is a right angle. B. The measure of angle Z is \( 45^\circ \). E. The perpendicular bisector of \( \overline{XZ} \) creates two smaller isosceles triangles.
-
gj bisects ∠fgh and is a perpendicular bisector of fh. what is true of …
It has exactly 3 congruent sides.
-
isosceles triangle abc has a perimeter of 96 centimeters. the base of t…
36 cm (corresponding to the option "36 cm")
-
consider the diagram and proof by contradiction. given: △abc with ∠b ≅ …
A. converse of the isosceles triangle theorem
-
what is always true about the angles of an isosceles triangle? all thre…
B. At least two of the angles are congruent.
-
triangle qst is isosceles, and \\(\\overline{rt}\\) bisects \\(\\angle …
A. \( m\angle QRT = 90^\circ \) B. \( m\angle QRT=m\angle SRT \)
-
the side lengths of triangle abc are written in terms of the variable p…
\( m\angle C > m\angle A > m\angle B \) (the third option: \( m\angle C > m\angle A > m\angle B \))
-
triangle xyz is shown, where n ≥ 5. image of triangle with vertices x, …
Angle \( X \) is the largest angle, Angle \( Z \) is greater than angle \( Y \), \( \overline{XZ} \) is the shortest side (i.e., the three true statements are: "Angle \( X \) is t…
-
in the diagram, mq = qp = po = on. if np is greater than mp, which must…
Angle O is larger than angle Q.
-
consider the triangles shown. if ( mangle utv < mangle uts < mangle str…
A. \( VU < US < SR \) by the hinge theorem.
-
4 jenn noticed that she can fit two juice boxes side by side on the bot…
The volume of the larger box is 6 juice - box units. ### Problem 5
-
gene starts from home and travels 3 miles north to the shopping mall. f…
at the mall
-
in the triangles, qr = de and sr = fe. which statement about the sides …
DF < QS (the option with "DF < QS")
-
which statement is true regarding triangle tuv? ○ angle t is the smalle…
Angle \(V\) is the smallest angle.
-
graph the solution to the compound inequality (-\frac{3}{5}s + 4 < 7) a…
First, solve each inequality: 1. Solve \(-\frac{3}{5}s + 4 < 7\): Subtract 4: \(-\frac{3}{5}s < 3\) Multiply by \(-\frac{5}{3}\) (reverse inequality): \(s > -5\) (open circle at \…
-
consider the triangle. which shows the order of the angles from smalles…
angle B, angle A, angle C
-
in the triangles, (overline{gk} cong overline{pn}) and (overline{hg} co…
Angle G is smaller than angle P.
-
the average length of a sports car is more than 13 and is less than or …
The correct graph is the one with an open circle at 13, a closed circle at 16.5, and a line segment connecting them (the first graph in the given options).
-
4 jenn noticed that she can fit two juice boxes side by side on the bot…
6 (juice box units) ### Problem 5 First, calculate the volume of this box. The volume of a rectangular box is given by \( V = l \times w \times h \), where \( l = 2 \) inches, \( …
-
22. what is the volume of soup that will fit in a cylindrical - shaped …
\( V=\pi r^{3}+2\pi r^{2} \) (the fourth option)
-
a statement is shown. if the base angles of a triangle are congruent, t…
If the base angles of a triangle are not congruent, then the triangle is not an isosceles triangle. (The fourth option)
-
if triangle def has a 90° angle at vertex e, which statements are true?…
B. The angle at vertex D is acute. D. Triangle DEF is a right triangle.
-
a triangle has side lengths measuring 3x cm, 7x cm, and h cm. which exp…
\(4x < h < 10x\) (corresponding to the first option)
-
triangle abc is an obtuse triangle with the obtuse angle at vertex b. a…
less than \(90^\circ\) (the option: less than \(90^\circ\))
-
steven is cutting an 11 ft piece of lumber into three pieces to build a…
The diagram with lengths 3 ft, 4 ft, and 4 ft (the fourth option) shows a way to cut the wood to form a triangle.
-
triangle qrs has the angle measures shown. what is the measure of the o…
108
-
identify the negation of each statement. ∠hjk and ∠ity are supplementar…
s: - Negation of “\(\angle HJK\) and \(\angle JTY\) are supplementary angles”: \(\boldsymbol{\angle HJK}\) and \(\boldsymbol{\angle JTY}\) are not supplementary angles. - Negation…
-
fionas school is in the shape of a triangle, with three hallways connec…
between 30 yards and 150 yards
-
consider the conditional statement, if the radius of a circle is 5, the…
A. The radius of a circle is 5 if and only if the diameter is 10.
-
for a craft project, four students each chose three pieces of wire from…
Sonji
-
a statement is shown. if a polygon has four congruent sides and four ri…
If a polygon is not a square, then it does not have four congruent sides and four right angles.
-
which statements about the diagram are true? select three options. □ de…
- \( DE + EF > DF \) - \( 5 < DF < 13 \) - \( \triangle DEF \) is a scalene triangle
-
diagram: triangle abc with points a, b, c. ab = 12, ac = 15, bc (dashed…
\(3\) (corresponding to the option "3")
-
fluency and skills practice breaking apart figures to find volume conti…
The volume of the figure is \(\boxed{175}\) cubic centimeters.
-
which are the possible side lengths of a triangle? ○ 3 cm, 5 cm, 9 cm ○…
B. 4 cm, 8 cm, 10 cm
-
let p, q, and r represent the following simple statements. p: i get an …
\( (p \vee eg q) ightarrow r \)
-
graph the image of δklm after a rotation 270° clockwise around the orig…
The image of $\triangle KLM$ after a 270° clockwise rotation around the origin has vertices at $K'(-9, 0)$, $L'(-6, 1)$, and $M'(-7, -1)$. (To graph, plot these points and connect…
-
which angle’s measure is equal to the sum of the measures of ∠bac and ∠…
\(\boldsymbol{\angle CBE}\)
-
a polygon has sides of length 24 feet, 22 feet, 21 feet, 26 feet, and 2…
116 feet
-
what is the value of k? ○ k=28 ○ k=29 ○ k=31 ○ k=42 (5k - 3)° (9 + k)°
\(k = 29\) (corresponding to the option \(k = 29\))
-
find the perimeter of the following figure. 5 ft rectangle 11 ft perime…
\( 32 \) square feet (Wait, no, perimeter of a rectangle is in linear units, so it should be \( 32 \) feet. The formula gives the perimeter as \( 2\times(11 + 5)=2\times16 = 32 \)…
-
classify the angle as acute, right, obtuse, or straight. diagram of ang…
B. obtuse
-
graph the image of △uvw after a translation 12 units left and 2 units d…
The translated triangle \( \triangle U'V'W' \) has vertices at \( U'(-9, 1) \), \( V'(-7, 1) \), and \( W'(-10, 7) \). (Graph by plotting these points and connecting them.)
-
13. find the total area of a round section of land that has a 2.5-foot-…
\( A = \pi r^{2}+5\pi r + 6.25\pi \) (the third option)
-
find the skating area shown to the right. use π≈3.14. the skating area …
\( 234.2 \) square meters (or if we consider that maybe the width is different, but based on the diagram, radius 4, so diameter 8, so the calculation is correct. Wait, maybe the l…
-
7. the volume (v) of a rectangular pyramid can be determined by using t…
$w = \frac{3V}{lh}$ (corresponding to the option $w=\frac{3V}{lh}$)
-
graph the image of △klm after a rotation 270° clockwise around the orig…
To graph the image of $\triangle KLM$ after a $270^\circ$ clockwise rotation around the origin, follow these steps: ### Step 1: Identify the coordinates of the vertices of $\trian…
-
find the unknown length in the right triangle. the unknown length is ap…
\( 6.928 \)
-
graph the image of △def after a reflection over the x-axis.
To graph the image of \( \triangle DEF \) after reflection over the \( x \)-axis: 1. **Identify Original Coordinates**: - \( D(-1, -8) \), \( E(-1, -4) \), \( F(8, -9) \) (from th…
-
graph the image of f(-1, 9) after a reflection over the y-axis.
The image of \(F(-1,9)\) after reflection over the \(y\) - axis is the point \((1,9)\). When graphing, plot the point with \(x = 1\) and \(y=9\).
-
4. evaluate $\\pi r^2$ when $r = 4.5$. use $3.14$ for $\\pi$. \\bigcirc…
63.585 (corresponding to the option with 63.585)
-
3. find the total area of a round section of land that has a 2.5-foot-w…
\( A = \pi r^2 + 5\pi r + 6.25\pi \) (the last option)
-
which statements are always true regarding the diagram? select three op…
- \( m\angle5 + m\angle6 = 180^\circ \) - \( m\angle2 + m\angle3 = m\angle6 \) - \( m\angle2 + m\angle3 + m\angle5 = 180^\circ \)
-
graph the image of △cde after a reflection over the x-axis.
The image of \( \triangle CDE \) after reflection over the \( x \)-axis has vertices at \( C'(-6, -6) \), \( D'(2, -6) \), and \( E'(-6, -3) \). (Graph by plotting these points an…
-
1. what is the volume of soup that will fit in a cylindrical - shaped c…
\( V = \pi r^{3}+2\pi r^{2} \) (the third option)
-
which statement about the value of x is true? ○ x > 38 ○ x < 39 ○ x < 7…
\( x>38 \) (the option " \( x>38 \)")
-
find the measures of angles x, y, and z in the figure. m||n. ∠x=□° ∠z=□…
\( \angle x = \boldsymbol{111}^\circ \) \( \angle z = \boldsymbol{111}^\circ \) \( \angle y = \boldsymbol{69}^\circ \)
-
graph the image of △uvw after a translation 12 units left and 2 units d…
The translated triangle \( \triangle U'V'W' \) has vertices at \( U'(-10, 1) \), \( V'(-7, 1) \), and \( W'(-10, 7) \). (Graphing these points on the coordinate plane completes th…
-
breaking apart figures to find volume continued 7 2 cm 2 cm 5 cm 2 cm 5…
Since the problem in question 9 refers to "the figure in problem 3" (which isn't shown here), we'll assume a general composite 3D figure (like a rectangular prism with parts added…
-
find the perimeter of the figure given to the right. use the approximat…
100.54
-
what are two different ways to break apart the figure in problem 3 to f…
Since the figure from problem 3 is not provided, we can't give a specific answer about it. However, in general, for composite 3D figures (like rectangular prisms combined or with …
-
graph the image of △jkl after a translation 6 units right and 9 units u…
The image of \( \triangle JKL \) has vertices at \( J'(1,0) \), \( K'(5,0) \) and \( L'(3,1) \). (To graph, plot these points and draw the triangle.)
-
find the perimeter of the figure given to the right. use the approximat…
100.54
-
unit 3 - logic and geometry 23 of 34 this quiz: 34 point(s) possible th…
The volume of the solid is \( 60 \) cubic inches.
-
6b. ray ab bisects ∠dac. solve for x. 6c. ray zx bisects ∠wxy. find m∠w…
\( x = 7 \) ### 6C
-
which represents an exterior angle of triangle abf? ∠bad ∠afe ∠cad ∠cab
\( \angle AFE \) (the option with \( \angle AFE \))
-
quiz: quiz unit 3 - logic and geometry find the area of the given geome…
\(258\) square meters
-
graph the image of △pqr after a translation 7 units left.
The translated triangle \( \triangle P'Q'R' \) has vertices at \( P'(-3,7) \), \( Q'(-3,8) \), \( R'(-4,9) \). (To graph, plot these points and draw the triangle.)
-
graph the image of square klmn after a translation 6 units left and 4 u…
The translated square has vertices at \( K'(-1, -1) \), \( L'(1, -1) \), \( M'(1, 1) \), \( N'(-1, 1) \). (Graphing these points on the coordinate plane as described completes the…
-
given: δabc prove: m∠zab = m∠acb + m∠cba we start with triangle abc and…
### First Dropdown (m∠ZAB + m∠CAB = 180° reason) ## Step1: Recall linear pair postulate A linear pair of angles is supplementary, meaning their measures sum to \(180^\circ\). Sinc…
-
unit 3 - logic and geometry 18 of 34 this quiz: 34 point(s) possible th…
First sub - question: B. $\angle QOP$ Second sub - question: C. $\angle SOR$
-
graph the image of △stu after a translation 3 units right and 10 units …
The translated triangle \( \triangle S'T'U' \) has vertices at \( S'(7, -8) \), \( T'(7, 0) \), and \( U'(-2, -8) \). (Graphing these points on the given coordinate plane will sho…
-
which statements are always true regarding the diagram? check all that …
\(m\angle3 + m\angle4 = 180^\circ\), \(m\angle2 + m\angle4 + m\angle6 = 180^\circ\), \(m\angle2 + m\angle4 = m\angle5\)
-
given: m || cb prove: m∠abc + m∠bac + m∠acb = 180° which statement just…
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
-
let w represent i wash my windows, let r represent it rains, and let t …
The first box should be filled with \( r \) and the second box should be filled with \( w \), so the symbolic statement is \( eg r \to w \).
-
graph the image of rectangle cdef after a translation 4 units left and …
The translated rectangle has vertices at \( \boldsymbol{F'(-10, 9)} \), \( \boldsymbol{E'(-6, 9)} \), \( \boldsymbol{D'(-6, 3)} \), and \( \boldsymbol{C'(-10, 3)} \). (Graph by pl…
-
34. ∠g and ∠h are complementary angles. if ( mangle g = (6x - 15)^circ …
\( 39^\circ \) ### Problem 35
-
identifying exterior angles of triangles which represents an exterior a…
$\angle JXZ$
-
solving for exterior angle measures what is the measure of ∠abd? ○ 27° …
\(114^{\circ}\) (corresponding to the option \(114^{\circ}\))