Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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larissa dives into a pool that is 8 feet deep. she touches the bottom o…
\(53.1^{\circ}\)
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the equation \\(cos^{-1}\\left(\\frac{3.4}{10}\ ight) = x\\) can be use…
C. $70^{\circ}$
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a right triangle has side lengths ac = 7 inches, bc = 24 inches, and ab…
\(m\angle A\approx73.7^{\circ},m\angle B\approx16.3^{\circ},m\angle C = 90^{\circ}\)
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which equation can be used to find the measure of angle gfe? $\\cos^{-1…
\(\cos^{-1}(\frac{11.9}{14.5})=\theta\) (the second option)
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apply your knowledge of reflections to answer each question below. a us…
1. \(J'(-7,-7)\), \(K'(-5,-2)\), \(L'(-2,-3)\) 2. \((x,y)\to(x, - y)\) 3. The transformation is a reflection over the \(y\) - axis (since the \(x\) - coordinates of the pre - imag…
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which equation can be used to solve for the measure of angle abc? \\( \…
\(\tan(x)=\frac{2.4}{10}\) (Option A)
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the length of the hypotenuse, line segment ac, in right triangle abc is…
\(53.1^{\circ}\)
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which equation can be used to find the measure of angle bac? $\\tan^{-1…
\(\tan^{-1}(\frac{12}{5})=x\) (the second option)
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drag the right word to its synonyms hint, mention, reference allusion j…
Drag "allusion" to the blue circle with "hint, mention, reference"
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which is the best approximation for the measure of angle xyz? 33.6° 39.…
\(39.8^{\circ}\)
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2. write an algebraic representation for the reflection. (x,y)→x,−y) b …
4. B. \((-x,y)\) 5. \((4,-8)\)
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rejoining the club one plus one equals two, a triangle has three sides,…
sarcastic, annoyed
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which equation can be used to solve for b? triangle with right angle at…
\(b=(8)\tan(30^{\circ})\) (the first option)
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right triangle abc is shown. which equation can be used to solve for c?…
\(\cos(50^{\circ})=\frac{3}{c}\) (the fourth option)
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right triangle abc is shown. which equation can be used to solve for c?…
\(\sin(50^{\circ})=\frac{3}{c}\) (the first option)
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which coordinate grid shown points whose coordinates have a proportiona…
The bottom - left coordinate grid (with points \((4,6)\), \((8,12)\), \((12,18)\))
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reflections apply your knowledge of reflections to answer each question…
1. \( J'(-7, 7) \), \( K'(-5, 2) \), \( L'(-2, 3) \) 2. \((x, y) \to (x, -y)\)
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rejoining the club one plus one equals two, a triangle has three sides,…
It paints a mental picture suggesting that scientists can still choose what to research despite having many options.
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a triangle has angles that measure 30°, 60°, and 90°. the hypotenuse of…
23.7 in.
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what is the approximate value of x? round to the nearest tenth. triangl…
4.6 cm
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use structure select the angles and sides of the triangle that are list…
B) ∠X, ∠Y, ∠Z, $\overline{YZ}$, $\overline{XZ}$, $\overline{XY}$
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there is a right triangle with right angle at the top left, vertex labe…
\(\cos(60^{\circ})=\frac{b}{a}\)
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there is a rectangle divided into two parts, each part is labeled a + 1…
\(2a + 2 = 32\)
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there is a right triangle with right angle at c, side length 5 cm (oppo…
\(\tan(30^{\circ})=\frac{5}{b}\) (the first option)
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which angles are corresponding angles? image of two parallel lines (uw …
$\angle UVX$ and $\angle TSQ$
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a triangle with right angle at c. side bc is 5 in. angle at b is 35 deg…
\(c=\frac{5}{\cos(35^{\circ})}\) (the second option)
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on the fourth day of christmas my true love gave to me. adjectives and …
1. Santa **carefully** wrapped the (colorful) gift with (shiny) paper and a (sparkly) bow. 2. The (tiny) elves waited **patiently** for the (delicious) cookies Mrs. Claus makes ev…
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shown below is a blueprint for a rectangular kennel at a pet hotel. wha…
74
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the equation \\(\\sin(40^\\circ) = \\frac{b}{20}\\) can be used to dete…
12.9 cm
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which angles are alternate exterior angles? options: ∠nmk and ∠opr ∠nmk…
∠NMK and ∠OPR
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which relationship in the triangle must be true? triangle with right an…
\(\sin(B)=\cos(90 - B)\)
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given right triangle jkl, what is the value of cos(l)? options: \\( \\f…
\(\frac{5}{13}\) (assuming a typo in the side - length \(KL\) as \(5\) instead of \(6\) to match the given options)
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given △def, which is not equal to cos(f)? sin(f). sin(d). tan(f). cos(d…
\(\tan(F)\)
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which angles are corresponding angles? ∠ihf and ∠ihk ∠lkh and ∠jkh ∠lkm…
∠IHF and ∠GHK
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given right triangle gyk, what is the value of tan(g)? options: $\frac{…
\(\sqrt{3}\)
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question 6 of 12, step 1 of 1 graph the solution to the given compound …
A number line with a closed circle at -9 shaded to the left and a closed circle at -4 shaded to the right.
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which angles are adjacent angles? options: ∠rqs and ∠mnl ∠mnl and ∠onl …
∠MNL and ∠ONL
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rt and uw are parallel lines. which angles are corresponding angles? ∠u…
∠UVS and ∠RSQ
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given right triangle mnl, what is the value of cos(m)? options: 3/5, 3/…
\(\frac{4}{5}\)
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which angles are consecutive interior angles? image of lines and angles…
∠FGJ and ∠KJG
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given right triangle def, what is the value of sin(e)? options: \\(\\fr…
\(\frac{3}{5}\) (the first option)
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which angles are consecutive interior angles? diagram with lines ln, oq…
∠QPM and ∠NMP
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x is the midpoint of \\(\\overline{uw}\\) and \\(\\overline{tv}\\). com…
For statement 4 (\(\overline{TX}\cong\overline{VX}\)), the reason is "Definition of midpoint". For statement 5 (\(\angle TXW\cong\angle UXV\)), the reason is "Vertical angles cong…
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given right triangle xyz, which correctly describes the locations of th…
\(a\) is adjacent, \(b\) is opposite, \(c\) is the hypotenuse.
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which angles are alternate interior angles? image of lines and angles o…
∠YXU and ∠TUX
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given right triangle pqr, which represents the value of sin(p)? options…
\(\frac{RQ}{PQ}\)
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qs and tv are parallel lines. which angles are adjacent angles? ∠srp an…
∠SRP and ∠SRU
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the relationship between the perimeter and side length of a regular oct…
The perimeter increases by 8 (the option corresponding to "The perimeter increases by 8").
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which trigonometric ratios are correct for triangle def? select three o…
\(\sin(D)=\frac{24}{25}\), \(\cos(E)=\frac{7}{25}\), \(\tan(D)=\frac{24}{7}\), \(\sin(E)=\frac{7}{25}\) are the relevant ratios. So the correct options are \(\sin(D)=\frac{24}{25}…
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given right triangle xyz, what is the value of tan(y)? options: \\(\\fr…
\(\frac{\sqrt{3}}{3}\) (the second option)
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the hypotenuse of a 45°-45°-90° triangle measures 128 cm. what is the l…
\(64\sqrt{2}\text{ cm}\) (the second option)
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a person is standing exactly 36 ft from a telephone pole. there is a 30…
\(12\sqrt{3}\text{ ft}\) (the second option)
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2 which model represents $4 \\times \\frac{2}{3}$? f two circles divide…
H.
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triangle mno is an equilateral triangle with sides measuring $16\\sqrt{…
24 units
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each leg of a 45°-45°-90° triangle measures 12 cm. what is the length o…
\(12\sqrt{2}\text{ cm}\)
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consider triangle qrs. the legs each have a length of 10 units. what is…
\(10\sqrt{2}\) units (the fourth option)
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what is the area, in square meters, of the shaded part of the rectangle…
130
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on the left, triangle pqr with pq = 20, qr = 8, angle at q. triangle st…
$\triangle STU\sim\triangle RQP$ by the SAS (Side - Angle - Side) similarity criterion. So the first blank is $RQP$ and the second blank is "SAS Similarity"
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4 which model represents \\(\\frac{3}{4}\\) of 28? (with images of mode…
The model which has \(21\) shaded circles (since \(\frac{3}{4}\times28 = 21\)) is the correct one.
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consider triangle ghj. what is the length of line segment hj? 5 units 5…
\(5\sqrt{3}\text{ units}\)
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figure q is the result of a transformation on figure p. which transform…
B. A reflection over the y - axis
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two triangles, △pqr and △stu. in △pqr, side pq is 20, side qr is 8, and…
△STU ~ △RQP by SAS similarity (or △STU ~ △PQR? Wait, no, let's confirm. Wait, maybe the correct triangle is △PQR. Wait, no, the ratios are 10/8=5/4 and 25/20=5/4, so ST=10, TU=25;…
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consider the incomplete paragraph proof. given: isosceles right triangl…
Determine the principal square root of both sides of the equation.
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a triangle abc with ac = 12, ab = 8, bc = 6. another triangle edf with …
Similar: $\triangle ABC \sim \triangle FDE$ by the SSS (Side - Side - Side) Similarity Criterion.
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a wall in marias bedroom is in the shape of a trapezoid. the wall can b…
\(13\) ft
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reflection across y=x e(1,-2) e(1,-2) e(-2,1) e(1,-4) e(1,2)
\(E'(-2,1)\)
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x y z n m not similar or not necessarily similar similar: △xyz ~ △□ by …
Similar: $\triangle XYZ \sim \triangle MNZ$ by the AA (Angle - Angle) Similarity Criterion.
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x is the midpoint of \\(\\overline{uw}\\) and \\(\\overline{tv}\\). com…
\(\angle T\cong\angle V\) is proved as above.
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there is a right triangle x y i with right angle at i, and another righ…
Similar: $\triangle XYZ \sim \triangle MZY$ (wait, maybe $\triangle XJY \sim \triangle MNY$) by the AA (Angle - Angle) Similarity Criterion. Wait, the correct triangles: $\triangl…
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two parallel lines are cut by a transversal as shown below. suppose m ∠…
\(m\angle5 = 76^{\circ}\) \(m\angle7=76^{\circ}\)
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the relationship between the perimeter and side length of a regular hex…
The perimeter increases by 6. (Corresponding to the option "The perimeter increases by 6")
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hangers graphs the hangers and the graph represent the same system of e…
$(1.5, 4.5)$
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x is the midpoint of \\(\\overline{uw}\\) and \\(\\overline{tv}\\). com…
| Statement | Reason | |---|---| | \(1\). \(X\) is the midpoint of \(\overline{UW}\) | Given | | \(2\). \(UX\cong WX\) | Definition of midpoint | | \(3\). \(X\) is the midpoint of…
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there are two triangles, triangle abc with sides ab=7, bc=8, ac=9, and …
Not similar or not necessarily similar
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m n y z x not similar or not necessarily similar similar: △xyz ~ △□ by …
$\triangle XYZ \sim \triangle MNY$ by the AA (Angle - Angle) Similarity Criterion (the first triangle should be $\triangle MNY$ or $\triangle MNM$ - correction: $\triangle XYZ \si…
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hk bisects ∠ihj and ( overline{hj} cong overline{hi} ). complete the pr…
1. Given; 2. Given; 3. Definition of angle bisector; 4. Reflexive property of congruence; 5. SAS (Side - Angle - Side) congruence; 6. CPCTC (Corresponding Parts of Congruent Trian…
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a b 15 12 9 c e 3 d 5 f 4 not similar or not necessarily similar simila…
Similar: $\triangle ABC \sim \triangle EFD$ by the SSS (Side - Side - Side) Similarity Criterion
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two parallel lines are cut by a transversal as shown below. suppose m∠2…
\(m\angle5 = 76^{\circ}\), \(m\angle7=76^{\circ}\)
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g i j 30° 50° h k l not similar or not necessarily similar similar: △jk…
Not similar or not necessarily similar
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the diameter of a circle is 16 yards. what is the circles area? round y…
201.06 square yards
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the radius of a circle is 19 feet. what is the circle’s area? round you…
1134.11
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s t 10 20 r 8 4 u p q not similar or not necessarily similar similar: △…
Similar: $\triangle STU \sim \triangle QPR$ (or appropriate labeled triangle) by the SAS (Side - Angle - Side) Similarity Criterion.
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$\\triangle tuw$ is equilateral, $\\angle vuw \\cong \\angle wtx$, and …
1. Given (definition of equilateral triangle) 2. Given 3. SAS 4. CPCTC 5. SAS 6. CPCTC
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the relationship between the perimeter and side length of a regular oct…
The perimeter increases by 8. (Corresponding to the option: The perimeter increases by 8)
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p q 4 10 r 5 15 6 t u not similar or not necessarily similar similar: △…
Similar: $\triangle STU \sim \triangle QRP$ (or $\triangle PRQ$) by the **SAS Similarity Criterion**
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m n y x z not similar or not necessarily similar similar: △xyz ~ △□ by …
Similar: $\triangle XYZ \sim \triangle MYN$ by the AA (Angle - Angle) Similarity Criterion.
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determining similarity decide whether the quadrilaterals are similar. e…
The quadrilaterals \(ABCD\) and \(FGHE\) are similar because all corresponding angles are equal (right angles) and the ratios of corresponding sides are equal (\(\frac{7}{3.5}=\fr…
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(a) use the calculator to find the area and circumference of the park. …
(a) Circumference: 113.04 yd; Area: 1017.36 yd² (b) Circumference (c) Area
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t is the midpoint of \\(\\overline{rs}\\). complete the proof that \\(\…
Right - angle congruence theorem (All right angles are congruent)
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(a) use the calculator to find the circumference and area of the mirror…
Circumference: 94.2 cm Area: 706.5 cm² (b) Area (c) Circumference
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find h to the nearest tenth. the length of h is approximately (round th…
\(108.3\)
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(a) use the calculator to find the circumference and area of the lawn. …
(a) Circumference: 276.32 ft; Area: 6079.04 ft² (b) Area (c) Area
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t is the midpoint of \\( \\overline{rs} \\). complete the proof that \\…
1. Reason: Given 2. Reason: Given 3. Reason: Definition of perpendicular (forms right angles) 4. Reason: Definition of midpoint 5. Reason: Reflexive property of congruence 6. Reas…
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find the missing length. the triangles in each pair are similar. 9) $\\…
\(\frac{169}{3}\)
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answer the questions about figure a and figure b below (a) which sequen…
(a) The correct option is: Dilate Figure A with scale factor $\frac{1}{2}$ centered at the origin, and then rotate that result counterclockwise 180° about the origin. (Also, if th…
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determine the length of the shortest side and the measure of the smalle…
The length of the shortest side (assuming AC is the shortest after measurement) is \(5.0\) cm and the measure of the smallest angle (assuming \(\angle B\) is the smallest after me…
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6. if cr = 28 inches, find the length of arc \\(\\overarc{bc}\\). 7. a …
Approximately \( 24.43 \) inches. ### Problem 7
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3. circle the consonant digraph in each word. a. ship b. shop c. dish
A. ship (circle "sh"), B. shop (circle "sh"), C. dish (circle "sh")
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write the coordinates of the vertices after a reflection over the x-axi…
\(J'(-5,10)\), \(K'(-5,5)\), \(L'(-2,1)\), \(M'(-2,6)\)
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write the coordinates of the vertices after a reflection over the y-axi…
\(B'(2,1)\), \(C'(3,8)\), \(D'(6,0)\)