Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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a right triangle has one leg measuring 9 units and a hypotenuse of 15 u…
\(\sqrt{144}\text{ or }12\)
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solve for x. x =
\(x = 4\)
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solve for x. x =
\(x = 12\)
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show what you know which of the following best describes the pythagorea…
The square of the hypotenuse is equal to the sum of the squares of the legs.
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4.7 understand: introduction to the pythagorean theorem show what you k…
10
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10. in the diagram below, if ( jl = 10x - 2 ), ( jk = 5x - 8 ), and ( k…
\(51\)
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start week 2 early: layla concluded: \i was able to map circle ( m ) on…
C. There is no error. This is a correct conclusion.
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mid-lesson checkpoint the cost of an adult ticket and 2 child tickets a…
The equation is $y + 2x = 55$. When an adult ticket ($y$) costs $25$, a child ticket ($x$) costs $15$.
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sidewalk shortcut at the park, you walk 6 blocks north, then 8 blocks e…
1. The shape is a right - angled triangle. 2. Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) where \(a = 6\) and \(b = 8\).
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mid-lesson checkpoint the cost of an adult ticket and 2 child tickets a…
The equation is \(y + 2x=55\). A child ticket costs $15.
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what is the value of x that makes the triangles similar?
\(22.5\)
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what does similarity require? same perimeter same shape and area equal …
Question 2: Equal angles and proportional side lengths Question 3: The image is similar to the original rectangle
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topic 2: segment addition postulate 9. if $df = 42$, find $de$. $7x + 1…
\(29\)
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based on the image, are triangles abc and xyz similar? yes, because the…
Yes, the side lengths are proportional.
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a fire truck extends a 100 foot ladder toward a building at a 75° angle…
$96.59$
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is figure abcd similar to figure efgh? select the correct answer. yes, …
No, because the figure is stretched vertically but not horizontally.
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use the diagram to the right to answer questions 5 - 8. 5. how many pla…
5. \(5\) 6. Plane \(ABCD\) (or other valid names) 7. Line \(AD\) 8. Point \(E\) (or \(C\) or \(D\))
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find the measure of x. 14 48° x =? round to the nearest hundredth.
$18.84$
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find the measure of x. 62° 8 x = ? round to the nearest hundredth
$17.04$
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three triangular shapes were measured by different students. analyze th…
False. Two triangles with the same three - angle measures are similar (by the AA (Angle - Angle) similarity criterion, since if two angles of one triangle are equal to two angles …
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what is sin a? 16 √87 13 sin a = ?
$\frac{13}{16}$
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lesson 1 | session 5 2 nautical flags are used to communicate on ships.…
Kimani needs \(225\) square inches of each color of fabric.
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topic 1: points, lines & planes use the diagram to the right to answer …
1. \(J\) and \(L\) 2. Line \(JL\) (or equivalent) 3. \(K\) 4. \(M\) (or \(N\))
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three triangular shapes were measured by different students. analyze th…
No, \(\triangle PQR\) cannot be similar to \(\triangle ABC\). The third - angle of \(\triangle ABC\) is \(60^{\circ}\) (using \(180-(60 + 60)\)), and the third - angle of \(\trian…
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laras soccer team has a pasta party once a month. lara used 8.5 pounds …
\(b < 8.5\) For graphing: - Plot an open circle at \(8.5\) (because \(b\) is not equal to \(8.5\)) on the number - line. - Draw a ray to the left of \(8.5\) (since \(b\) is less t…
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reggie is making balloon animals to sell at gardenburys summer carnival…
The inequality that models the story is \(b\geq17\). To graph \(b\geq17\), we first plot a closed circle at 17 (because 17 is included in the solution set, since it's "no fewer th…
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3 the scale from a garden to this drawing is 8 ft to 1 cm. the scale fr…
D. \(9.6\mathrm{cm}\) and \(14.4\mathrm{cm}\)
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a fire truck extends a 75 foot ladder toward a building at a 58° angle …
\(39.74\)
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question 4 is it possible for two triangles to be similar but not congr…
Yes, it is possible for two triangles to be similar but not congruent. For example, consider \(\triangle ABC\) and \(\triangle XYZ\). In \(\triangle ABC\), if \(\angle A = 60^{\ci…
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a 50 foot rope on a dock is connected to a boat at a 35° angle with the…
$40.96$
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mona and her sister, kaylee, collect tiny pets animal figurines. mona h…
The inequality that models the story is \(a < 27\). For graphing, we plot an open - circle at 27 (because \(a\) cannot be equal to 27) and draw an arrow to the left (towards the s…
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find the measure of x. round to the nearest hundredth.
$15.36$
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franklin is a member of his schools drama club. everyone in the club is…
\(t\geq35\) For graphing: - Plot a closed - circle at \(t = 35\) (because 35 is included in the solution set, as \(t\) can be equal to 35). - Draw an arrow to the right (because \…
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ernest is making a seashell frame for his moms birthday gift. he plans …
The inequality that models the story is \(w\leq14\). For graphing: - Plot a closed circle at \(14\) (because \(w = 14\) is allowed as per \(w\leq14\)). - Draw a ray to the left (s…
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use pascals triangle to expand $(2 + 3y)^{4}$. $(2 + 3y)^{4}=\\square$
\(16 + 96y+216y^{2}+216y^{3}+81y^{4}\)
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charlie and his younger brother, peter, are comparing their baseball ca…
\(p < 65\) For graphing: - Plot an open circle at \(65\) (because \(p\) is not equal to \(65\), just less than). - Draw a ray to the left (towards smaller numbers) from the open -…
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three triangular shapes were measured by different students. analyze th…
The scale factor is \(\frac{2}{3}\) and the length of \(BC\) is \(\frac{40}{3}\mathrm{cm}\approx13.33\mathrm{cm}\)
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greenville has a town - wide hunt for plastic dinosaur eggs every sprin…
The inequality is \(e>25\). For the graph, place an open - circle at 25 on the number line and draw a ray extending to the right.
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determine the perimeter and the area of the following triangles: a) 2.1…
a) Perimeter: \(13.49\space m\), Area: \(5.775\space m^{2}\) b) Perimeter: \(204.85\space cm\), Area: \(1800\space cm^{2}\)
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ks step statement reason 1. (overline{es}paralleloverline{hp}) given 2.…
The reason for step 3 is that $\angle Q$ is common to both triangles. So the statement for step 3 is $\angle Q\cong\angle Q$ (Common Angle).
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last year, emmas scout troop sold 504 boxes of cookies. this year, her …
The inequality that models the story is \(b>504\). On the number - line, there is an open circle at 504 and an arrow pointing to the right.
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the chapman family is taking a road trip to oregon this summer. mr. cha…
The inequality that models the story is \(m\geq150\). For the graph, we plot a closed - circle at \(150\) (because \(150\) is included in the solution set, since it's "at least 15…
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m∠eqp = m∠hgs + 30 ratio of similarity m∠eqp < m∠hgs + 30 triangle ineq…
\(\frac{QE}{GH}=\frac{QP}{GS}\) (Ratio of Similarity)
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complete the proof showing that the triangles \\( \\triangle ghs \\) an…
Since \(\frac{GH}{QE}=\frac{GS}{QP}=\frac{1}{2}\) and \(\angle HGS=\angle EQP = 58^{\circ}\), by the Side - Angle - Side (SAS) Similarity Theorem, \(\triangle GHS\sim\triangle QEP…
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are triangle abc and triangle def similar? explain your reasoning.
No, Triangle \(ABC\) and Triangle \(DEF\) are not similar because their corresponding angles are not equal.
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solve the inequality and graph the solution. -3u + 4 > 10 to draw a ray…
The solution of the inequality is \(u < - 2\). On the number - line, there is an open circle at \(-2\) and the ray extends to the left.
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solve the inequality and graph the solution. 2a - 1 < -9 to draw a ray,…
The solution of the inequality is \(a < - 4\). On the number - line, we have an open circle at \(-4\) and an arrow pointing to the left.
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given rectangle ( ghij ) below, ( hk = 70 ). if ( gi = x - 5 ), solve f…
\(x = 145\)
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given rectangle uvwx below. if wy = 16, find vx. answer attempt 1 out o…
\(32\)
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solve the inequality and graph the solution. 7g - 7 ≤ 7 to draw a ray, …
The solution of the inequality \(7g - 7\leq7\) is \(g\leq2\). On the number - line, we plot a closed circle at \(2\) (since the inequality includes equality, i.e., \(g = 2\) is pa…
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solve the inequality and graph the solution. 5y - 4 ≥ 6 to draw a ray, …
The solution of the inequality \(5y - 4\geq6\) is \(y\geq2\). On the number - line, we have a closed circle at \(2\) and an arrow pointing to the right.
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solve the inequality and graph the solution. 2 + 2u ≤ -2 to draw a ray,…
The solution of the inequality \(2 + 2u\leq -2\) is \(u\leq - 2\). On the number - line, we have a closed circle at \(-2\) and an arrow pointing to the left.
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dada la función lineal representada gráficamente a continuación, halla …
La pendiente de una recta paralela a la dada es \(-\frac{1}{2}\)
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solve the inequality and graph the solution. -3 + 2t > 1 to draw a ray,…
The solution of the inequality is \(t>2\). On the number - line, we plot an open circle at \(t = 2\) (because \(t = 2\) is not included in the solution) and draw a ray to the righ…
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solve the inequality and graph the solution. 3r + 9 ≥ 3 to draw a ray, …
The solution of the inequality \(3r + 9\geq3\) is \(r\geq - 2\). On the number - line, there is a closed circle at \(-2\) and an arrow pointing to the right.
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solve the inequality and graph the solution. 1 + 3f > 10 to draw a ray,…
The solution of the inequality \(1 + 3f>10\) is \(f>3\). On the number - line, there is an open - circle at \(3\) and an arrow pointing to the right.
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3. given: ab ≅ cg, ab || cg prove: △bca ≅ △gac statements reasons
| Statements | Reasons | |--|--| | \(AB\cong CG\) | Given | | \(AB\parallel CG\) | Given | | \(\angle BAC=\angle GCA\) | Alternate - interior angles (parallel lines \(AB\) and \(C…
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solve the inequality and graph the solution. 2v + 7 ≥ -5 to draw a ray,…
The solution of the inequality \(2v + 7\geq - 5\) is \(v\geq - 6\). On the number - line, we have a closed circle at \(-6\) and a ray extending to the right.
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a catering company gets an order to serve triangular cheese wedges at a…
Each angle measure is \(60^{\circ}\)
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solve the inequality and graph the solution. 2(w + 4) > 10 to draw a ra…
The solution of the inequality \(2(w + 4)>10\) is \(w>1\). On the number - line, there is an open - circle at \(1\) and an arrow pointing to the right.
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in a right triangle, one leg is 12 feet and another leg is 16 feet. wha…
20
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solve the inequality and graph the solution. 5 + 2c < 9 to draw a ray, …
The solution of the inequality \(5 + 2c<9\) is \(c < 2\). On the number - line, we plot an open circle at \(2\) (because \(c\) is not equal to \(2\)) and draw an arrow to the left…
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2. complete the creation as directed. 3. reflect on your creation. simi…
Yes, Triangle \(ABC\) and Triangle \(XYZ\) are similar. By the AA (Angle - Angle) similarity criterion, since \(\angle A=\angle X\), \(\angle B=\angle Z\), and \(\angle C=\angle Y…
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2. given: ( ac cong pc ), ( bc cong qc ) prove: ( \triangle abc cong \t…
$\triangle ABC\cong\triangle PQC$ by the SAS (Side - Angle - Side) congruence criterion.
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select the correct answers from each drop - down menu.this construction…
\(\frac{CE}{DC}\), \(BC\), \(\frac{BC}{DC}\)
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5. ( ab = ad + db )( cb = ce + eb )segment addition6. ( \frac{ad + db}{…
C. \(\frac{AB}{DB}=\frac{CB}{EB}\)
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similarity, proportion, and triangle proofs: mastery 11. ( ab^{2}=ac\ti…
B. \(\angle BCA\cong\angle DCB\)
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10. the figure below shows four congruent semicircles that touch only a…
G. \(48\pi\)
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in a right triangle, one leg is 9 feet and another leg is 15 feet. what…
17.5
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solve the inequality and graph the solution. 3y + 1 > 10 to draw a ray,…
The solution of the inequality \(3y + 1>10\) is \(y>3\). On the number - line, there is an open circle at \(3\) and a ray extending to the right.
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which figures show that st || qr?
The first figure shows that \(ST\parallel QR\)
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the formula for surface area for a cylinder can be manipulated and appl…
122.46
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a free kick is given in a soccer game where the player taking the kick …
A. 16 yards
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the formula for surface area for a cylinder can be manipulated and appl…
\(6.08\)
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choose the correct unit for each measurement. then write your answer. l…
11a. square units 11b. linear units
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1 choose the correct unit for each measurement. then write your answer.…
1a. square units 1b. linear units
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the pythagorean theorem can be modified in relationship to an oval shap…
\(10.4\)
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mark each statement about the parallelogram as true or false. 2a. to ca…
2a. False 2b. False 2c. True 2d. True
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match each graph to a situation. 1 the graph represents the perimeter, …
1. C 2. A 3. D 4. B
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the proof that \\( \\triangle mng \\cong \\triangle kjg \\) is shown. g…
AAS
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5) 4\\sqrt{320} find the missing side of each triangle. 6) 8 10 x
\(x = 6\)
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two rigid transformations are used to map △abc to △qrs. the first is a …
a rotation about point \(B\)
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the area of a triangle is 67 square feet. the base is twice the height.…
\( 8.2 \)
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triangle congruence what additional information is needed to prove that…
\(\angle LOA\cong\angle LMA\)
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the proof that ( \triangle qpt cong \triangle qrt ) is shown. given: ( …
definition of perpendicular bisector
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what is the area of a rectangle measuring 39 inches by 94 inches? you d…
3666
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rectangle congruence rectangle abcd is congruent to rectangle uhrt what…
\(144\mathrm{mm}^2\)
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a = 7 yards b = 14 yards c = 13 yards you only need to enter the final …
\(45.2\)
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triangle congruence is △mnl ≅ △qnl? why or why not? no, ∠m is not congr…
Yes, they are congruent by either ASA or AAS.
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which rigid transformation(s) can map (\triangle mnp) onto (\triangle t…
translation, then rotation
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1. what is the circumference, in inches, of a circle with a radius of 8…
1. D. \(16\pi\) 2. G. \(14\pi\) 3. C. \(80\)
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determine the area of the shape below. you only need to enter the final…
98
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given: \\( \\overline{rs} \\) bisects \\( \\angle mrq; \\angle rms \\co…
\( \triangle RMS\cong\triangle RQS \) by \( AAS \)
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geometry © 2025 kuta software llc. all pythagorean/radicals review simp…
\(6\sqrt{42}\) (because \(42\) has no perfect - square factors other than \(1\), so the expression \(6\sqrt{42}\) is already in its simplest form)
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what is the area of a triangle with a base length of 18 meters and a he…
117
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3. a model ship is built to a scale of 1 cm represents 5 meters. the le…
The length of the actual ship is \( 150 \) meters.
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complete each two - column proof. 1. given: ( kccong ba,akcong cb ) pro…
| Statements | Reasons | |---|---| | \(KC\cong BA\), \(AK\cong CB\) | Given | | \(AC = AC\) | Reflexive Property of Congruence | | \(\triangle ABC\cong\triangle CKA\) | SSS Congru…
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in △xyz, ( mangle x = 90^{circ} ) and ( mangle y = 30^{circ} ). in △tuv…
No congruency statement can be made because the side lengths are unknown.
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three quadrilaterals exist such that ( g h j k cong a s d f ) and ( g h…
\(\overline{AF}\)
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two sides and the non - included right angle of one right triangle are …
A. AAS