Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
-
for each figure below, determine if it has rotational symmetry. if it d…
### For the "5" - shaped figure: Rotational symmetry? No Angle? (No valid angle as it has no rotational symmetry) ### For the star - shaped figure: Rotational symmetry? Yes Angle?…
-
find m∠c. write your answer as an integer or as a decimal rounded to th…
\( 47.3 \)
-
points a and b are separated by a lake. to find the distance between th…
\(356.10\)
-
what is the radius of a circle whose equation is ((x + 5)^2 + (y - 3)^2…
B. 4 units
-
find ( mangle e ). write your answer as an integer or as a decimal roun…
\( 35.2 \)
-
which of the following transformations carry this regular polygon onto …
rotation of \( 60^\circ \) counterclockwise, reflection across \( l \)
-
describe the possible lengths of the third side of the triangle given t…
\(6<x<30\)
-
the length of a rectangle is 1 m more than twice the width, and the are…
Length: \( 10 \) m Width: \( 4.5 \) m
-
based on the given diagram, complete the sentence below. answer attempt…
incenter
-
look at the diagram. which term describes \\(\\overline{qs}\\)? \\(\\qu…
none of these
-
w is the midpoint of \\(\\overline{uv}\\) and \\(\\overline{uv} \\perp …
1. Definition of midpoint 2. Definition of perpendicular lines 3. Reflexive property of congruence 4. \(SAS\) (Side - Angle - Side) 5. \(CPCTC\) (Corresponding Parts of Congruent …
-
graph the point (-1.5, 4.5) on the coordinate plane.
The point \((-1.5,4.5)\) is plotted at the location 1.5 units left of the origin on the x - axis and 4.5 units up on the y - axis (mid - way between \(-2\) and \(-1\) on the x - a…
-
△abc and △xyz are similar. find the missing side length. (the triangles…
21
-
the path of a satellite orbiting the earth causes it to pass directly o…
distance from \(A\approx483.66\) km, height\(\approx482.79\) km
-
question 7 (multiple choice worth 4 points) (04.03r mc) calculate the a…
18 square units
-
determine if the two triangles are congruent. if they are, state the po…
The two triangles (\( \triangle ABC \) and \( \triangle DBC \)) are congruent by the SSS (Side - Side - Side) Congruence Postulate.
-
type the correct answer in the box. use numbers instead of words. each …
25
-
question determine if the two figures below are congruent. use the drop…
The two figures are congruent because only rigid motions are used to map Figure 1 onto Figure 2. Point corresponding to point U: M
-
find the value of x. enter the correct number in the box. show hints x …
\(80\)
-
find the orthocenter of the triangle with the given vertices. 12. n(-1,…
The orthocenter of triangle \( NPQ \) is \( (1,1) \) ### Problem 13:
-
of the orthocenter are (1, 3). triangle fgh has coordinates f(-3, 1), g…
\( x = 2 \) ### Problem 10:
-
in △hjk, hd = 21 and bk = 18. find each length. 5. hb 6. bd 7. ck 8. cb
s: 5. \( \boldsymbol{14} \) 6. \( \boldsymbol{7} \) 7. \( \boldsymbol{27} \) 8. \( \boldsymbol{9} \)
-
in △qrs, rx = 48 and qw = 30. find each length. 1. rw 2. wx 3. qz 4. wz…
1. \( RW = 32 \) 2. \( WX = 16 \) 3. \( QZ = 45 \) 4. \( WZ = 15 \)
-
look at the diagram. which term describes \\(\\overline{bd}\\)? perpend…
median
-
look at the diagram. which term describes \\(\\overline{qs}\\)? median …
altitude
-
look at the diagram. which term describes \\(\\overline{hj}\\)? \\(\\qu…
angle bisector
-
look at the diagram. which term describes \\(\\overline{df}\\)? perpend…
none of these
-
look at the diagram. which term describes \\(\\overline{df}\\)? perpend…
none of these
-
look at the diagram. which term describes \\(\\overline{xz}\\)? perpend…
median
-
∠acd is a right angle. which term describes \\(\\overline{ac}\\)? optio…
altitude
-
rejoining the club one plus one equals two, a triangle has three sides,…
B. By expressing that Pluto is the "lonely onlooker," the author is using personification to urge critics to restore Pluto’s status.
-
translation:(x,y)->(x-3,y-2) h(1,1) h(1,4) h(-2,-1) h(-2,3) h(-1,2)
\(H'(-2,-1)\) (the blue - colored option)
-
$$overline{xy} cong overline{wy}$$ and $$overline{uy} cong overline{vy}…
1. Given 2. Given 3. Vertical Angles Theorem 4. SAS (Side - Angle - Side) Congruence Criterion 5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
-
question 9 (multiple choice worth 4 points) (04.01r lc) if triangle jkl…
At least two sides are congruent.
-
find cosθ, where θ is the angle shown. give an exact value, not a decim…
$\frac{\sqrt{39}}{8}$
-
type the correct answer in the box. use numbers instead of words. each …
48
-
decide whether the triangles are similar. if they are, write a similari…
Similar: $\triangle ABC \sim \triangle DEF$ by the SSS (Side - Side - Side) Similarity Criterion
-
figure wxyz is a parallelogram which angle measures are correct? select…
$m\angle X = 55^{\circ}$, $m\angle W = 125^{\circ}$, $m\angle Z = 55^{\circ}$
-
question which segment is opposite to ∠s? answer \\overline{wy} \\overl…
$\overline{WY}$
-
given right triangle rst, what is the value of sin(s)? options: - \\(\\…
\(\frac{5}{13}\) (corresponds to the first option)
-
a garden is designed in the shape of a rhombus formed from 4 identical …
\(120\) ft
-
module 2 topic 1 assessment review 1. consider the circle on the right …
\(114^{\circ}\)
-
a certain regular polygon is rotated 240° about its center, which carri…
hexagon
-
which concept can be used to prove that the diagonals of a parallelogra…
congruent triangles
-
5. choose the correct answer. apply the 45°-45°-90° triangle theorem to…
for Question 5: The correct option is 7 cm (assuming the approximation, as \(5\sqrt{2}\approx7.07\)).
-
1. choose the correct answer. a pythagorean triple is a a set of three …
The option with "nonzero" (the second radio button option, assuming the first is "irrational" and the second is "nonzero" based on the text)
-
∠rtu and ∠vts are vert. ∠s 3. ∠rts ≅ ∠vtu, ∠rtu ≅ ∠vts 3 vertical angle…
\(\triangle RTS\cong\triangle VTU\) and \(\triangle RTU\cong\triangle VTS\)
-
law of sines: $\frac{sin(a)}{a} = \frac{sin(b)}{b} = \frac{sin(c)}{c}$ …
\(\frac{\sin(76^{\circ})}{2.6}=\frac{\sin(53^{\circ})}{z}\) (the fourth option)
-
statements reasons 1 \\(\\overline{ab} \\cong \\overline{cd}, \\overlin…
SSS congruency theorem
-
question which angle of rotation would carry an equilateral triangle on…
\(240^{\circ}\)
-
1. in parallelogram lonm, what is om? (2x + 3) cm, (3x - 6) cm options:…
D. \(34\space cm\)
-
which transformation will not carry the rectangle below onto itself? an…
a reflection over the \(x\) - axis
-
statements reasons 1 ad ≅ bc, ad || bc 1 given 2 ∠cad and ∠acb are alte…
CPCTC
-
what is the perimeter of parallelogram lmno? 18 cm 22 cm 40 cm 80 cm
\(80\) cm (the fourth option)
-
9) choose the best answer. apply the 30°-60°-90° triangle theorem. what…
\(a = 7\) inches, \(b = 7\sqrt{3}\) inches (or \(b \approx 12.12\) inches)
-
7) choose the best answer. apply the 30°-60°-90° triangle theorem to fi…
8 inches (the option with "8 inches") ### Question 8
-
marie and jake both set up a proportion to find the missing width, w, o…
Marie did not multiply 2·6 correctly.
-
5) choose the best answer. apply the 45°-45°-90° triangle theorem. if t…
\(\approx 5\) cm (the option with \(\approx 5\) cm) ### Question 6
-
what is the measure of angle l in parallelogram lmno? 20° 30° 40° 50°
\(40^{\circ}\)
-
the fence around a circular garden is 18 feet long. what is the area of…
26
-
3) choose the best answer. a 45°- 45°-90° right triangle is also called…
A. isosceles ### Question 4
-
practice problems 7 problems 1 a triangle has sides with lengths 8, 15,…
a. The triangle is a right - triangle because \(8^{2}+15^{2}=17^{2}\) (i.e., \(64 + 225=289\)). b. The acute angles are approximately \(28.1^{\circ}\) and \(61.9^{\circ}\)
-
which transformation will not carry the square below onto itself? answe…
a reflection over the line \(y=-x + 5\)
-
alicia has molds to make ice cubes in the shapes of two pyramids that h…
The volume of ice in shape 1 is \(20\) cubic centimeters. The volume of ice in shape 2 is \(10\) cubic centimeters. Shape 1 contains twice as much ice as shape 2. Alicia is not co…
-
which side in △xgr corresponds with side rz? which side in △rpz corresp…
RX RP $\frac{1}{4}$
-
1) match. the 45°-45°-90° triangle theorem states that in a 45°-45°-90°…
First blank: b. congruent; Second blank: a. \( \sqrt{2} \) ### 2)
-
what compass heading represents 45° east of south? ?° hint: compass hea…
135
-
which transformation would take figure a to figure b? answer a reflecti…
A reflection over the \(x -\)axis
-
the right triangle pqr is shown. if the dimensions of δpqr are multipli…
The hypotenuse of △P'Q'R' has a measure of 24"
-
triangle abc was dilated to form triangle jkl. which statement appears …
△JKL is an enlargement of △ABC
-
marie and jake both set up a proportion to find the missing width, w, o…
Marie did not set up the proportion correctly.
-
6) choose the correct answer. image of a triangle with sides labeled √1…
acute (the option corresponding to "acute")
-
determine the coordinates of point k so that quadrilateral abdc is simi…
(7,10)
-
question what is the image point of (-2, -7) after a translation right …
\((2,-9)\)
-
question what is the image point of (-8, 7) after a translation right 5…
\((-3,12)\)
-
5) choose the correct answer. image of triangle with vertices c, b, a; …
A. right
-
example 3 find the range of possible values for x. 5. there is a geomet…
$6.5 < x < 18.5$
-
question what is the image point of (-7, 4) after a translation left 3 …
\((-10,9)\)
-
4) choose the correct answer. image of triangle def with sides: de=6 cm…
obtuse (the option with "obtuse" as the text, so the second option: obtuse)
-
what compass heading represents 40° east of south? ?° hint: compass hea…
\(220\)
-
3) choose the correct answer. a pythagorean triple is a set of three no…
A. whole
-
question find the values of x and y answer attempt 2 out of 5 x = y =
\(x = 80\), \(y = 50\)
-
directions: answer the following questions to the best of your ability.…
enlarge, reduce ### Question 2
-
answer the following questions. 1) choose the correct answer. the conve…
D. right
-
question find the values of x and y (image of a right triangle with a s…
\(x = 130\), \(y = 50\)
-
question reflect the figure over the line ( y = -2 ). plot all of the p…
Plot the new triangle with vertices obtained by using the rule \((x,y)\to(x,-4 - y)\) for each vertex of the original triangle.
-
ab = \\square redondea tu respuesta a la centésima más cercana. (right …
\( AB \approx 4.73 \) (redondeado a la centésima)
-
23 which of these equations is equivalent to $6\\frac{3}{4} \\times 3\\…
B. \(19 \div 3\frac{1}{4} = 6\frac{3}{4}\)
-
18. match the correct answers. $overline{gi} cong overline{jl}, overlin…
Left: a. \(HI\), Right: d. \(KL\)
-
what compass heading represents 50° north of east? ?° hint: compass hea…
40
-
17. match the correct answers. ac ≅ df, bc ≅ ef, and ab > de according …
First blank: d. $\angle C$, Second blank: b. $\angle F$
-
15. choose the correct answer. 1. 8 cm 2. 4 cm 3. 3 cm the set of line …
does not ### Question 16
-
14. order the angles of △ghi from smallest to largest.
\(\angle I\), \(\angle G\), \(\angle H\)
-
13. order the sides of $\\triangle def$ from shortest to longest. (imag…
\(\overline{DF}\), \(\overline{EF}\), \(\overline{DE}\) (or \(b\), \(c\), \(a\))
-
4. is this shape a quadrilateral? how do you know?
Yes, this shape is a quadrilateral because it is a closed figure with 4 straight sides.
-
use the information provided to answer part a and part b for question 2…
\(2.6\)
-
what compass heading represents 17° south of west? ?° hint: compass hea…
287
-
incorrect 2 tries left. please try again. flight two planes take off fr…
The second plane; the legs are congruent. If $x < 30$, then the measure of the included angle, $(180 - x)^\circ$, is greater for the second plane; so, by the Hinge Theorem, the se…
-
8. △abc is dilated from center a by a factor not equal to 1 to form △ak…
A. \(\overline{AB}\) and \(\overline{AK}\) lie on the same line. B. The line containing \(\overline{BC}\) is parallel to the line containing \(\overline{KL}\). D. \(\angle ABC\con…
-
17. a dilation with a center at p(0, 0) and a scale factor k is applied…
B. If \(k>1\), then \(M'N'>MN\); C. If \(0 < k<1\), then \(M'N'<MN\); E. If \(k = 1\), then \(M'N'=MN\); F. If \(k = 0.5\), then \(M'N'=0.5(MN)\)