Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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20. find the perimeter and area of the rectangle. 2.1 mm 3.9 mm
Perimeter: $12$ mm, Area: $8.19$ mm²
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19. find the perimeter and area of this triangle.
Perimeter = $40$, Area = $56$
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to consider two triangles, first answer part a. then, answer part b. pa…
\(x = 12\), \(y = 6\)
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proof complete the two - column proof by dragging the missing statement…
| Statements | Reasons | | --- | --- | | 1. \(\angle A\cong\angle C\), \(\angle D\cong\angle B\) | 1. Given (first use) | | 2. \(\angle AED\cong\angle CEB\) | 2. Vertical angles a…
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consider △abc ~ △xyz. what is the value of tan(a)? 3/4 what is the valu…
s: - $\tan(X)$: $\frac{3}{4}$ - Relationship: The two tangent ratios are equal (both $\frac{3}{4}$)
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consider δabc ~ δxyz. what is the value of tan(a)? what is the value of…
\(\frac{3}{4}\)
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4.1 translations (pp. 173-180) graph quadrilateral abcd with vertices a…
s: 1. \(X'(2,5)\), \(Y'(-3,4)\), \(Z'(-4,-1)\) 2. \(X'(-1,3)\), \(Y'(-6,2)\), \(Z'(-7,-3)\) 3. \(X'(5,2)\), \(Y'(0,1)\), \(Z'(-1,-4)\) 4. \(X'(6,4)\), \(Y'(1,3)\), \(Z'(0,-2)\) 5.…
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step 12b: now, well use the following multiple - choice question (and i…
In option D, the word "uniform" can be circled as a misleading word. (Or other words like "commonplace" in A, "momentous" in B, "known" in C can also be considered depending on in…
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consider △lmn. m∠l + m∠m = 90° sin(l) = sin(m) = cos(l) cos(m) cos(n)
For $\sin(L)$: $\cos(M)$ (but wait, the options are $\cos(L)$, $\cos(M)$, $\cos(N)$). Wait, no, let's check the triangle again. $\angle L = 42^{\circ}$, so $\sin(L)=\sin(42^{\circ…
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consider △lmn. m∠l + m∠m = \\boxed{\\quad}^\\circ sin(l) = \\boxed{\\qu…
For \(m\angle L + m\angle M\), the value is \(\boldsymbol{90}\).
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consider △xyz what are the ratios of sine, cosine, and tangent for angl…
The correct option is \(\boldsymbol{\sin(Y)=\frac{XZ}{XY};\cos(Y)=\frac{YZ}{XY};\tan(Y)=\frac{XZ}{YZ}}\) (the third option among the given options).
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1. δ qrs is graphed in the coordinate plane. δ qrs is the image of δ qr…
To graph \( \triangle Q'R'S' \) (the reflection of \( \triangle QRS \) over the \( y \)-axis), follow these steps: 1. **Identify Original Coordinates** (from the graph): - \( Q(-1…
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try it what are the input and output values for determining the sine of…
B. input: $60^\circ$; output: $\frac{\sqrt{3}}{2}$
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create similar right triangles by changing the scale factor of the righ…
s: - When scale factor is 1: \(\frac{1}{2}\) - When scale factor is 3: \(\frac{1}{2}\) - For any \(30^\circ\) angle: \(\frac{1}{2}\)
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complete the table to show the name of each side of the right triangle …
| | $a$ | $b$ | $c$ | |-------|--------------|--------------|--------------| | $\angle A$ | Opposite Side | Adjacent Side | Hypotenuse | | $\angle B$ | Adjacent Side | Opposite Si…
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what are the lengths of the other two sides of the triangle? ac = 5 and…
AC = 5 and BC = \(5\sqrt{3}\) (the last option: AC = 5 and BC = \(5\sqrt{3}\))
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which triangle is a 30°-60°-90° triangle? 10 5 5√3 15 5 5√3 10 5 10√3 1…
The first triangle (with sides 5, \(5\sqrt{3}\), 10)
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consider triangle pqr. what is the length of side qr? 8 units 8√3 units…
16 units
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the height of trapezoid vwxz is $8\\sqrt{3}$ units. the upper base, $\\…
8 units (but since the second part's options include 18, and the process for YX: from \(30 - 60 - 90\) triangle, longer leg \(=8\sqrt{3}\) (opposite 60°), so shorter leg (YX) \(=\…
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a wall in marias bedroom is in the shape of a trapezoid. the wall can b…
13 ft (corresponding to the option "13 ft")
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isaiah sketches a model of a skateboard ramp. the model has two surface…
$\boldsymbol{4\sqrt{2}}$ in. (Corresponding to the option with $4\sqrt{2}$ in.)
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consider that △abc is an equilateral triangle, and (overline{ad}) is a …
1. First blank (in \( \square^2 + (AD)^2=(2x)^2 \)): \( x \) 2. Second blank (in \( \square x^2 - x^2 \)): \( 4 \) (since \( (2x)^2 = 4x^2 \)) 3. Third blank (in \( (AD)^2=\square…
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from the side view, a gymnastics mat forms a right triangle with other …
\(\frac{5\sqrt{3}}{3}\) ft (corresponding to the option \(\boldsymbol{\frac{5\sqrt{3}}{3}}\) ft)
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second base third base first base 90 ft home plate a baseball field is …
\(90\)
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complete the proof that $\\triangle efh \\cong \\triangle eig$. | state…
Angle - Angle - Side (AAS) Congruence Theorem
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triangle abc is an equilateral triangle. segment ad measures 18 inches.…
The correct statements are: - \(DC = 6\sqrt{3}\) in. - \(AC = 12\sqrt{3}\) in.
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complete the proof that $\\triangle rvx \\cong \\triangle twu$. | state…
AAS (Angle - Angle - Side) Congruence Theorem
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the hypotenuse of a 45°-45°-90° triangle measures 24 inches. what is th…
\(12\sqrt{2}\) in. (corresponding to the option: \(12\sqrt{2}\) in.)
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determining angle/side relationships what are the angle measures in tri…
\( m\angle A = 90^{\circ}, m\angle B = 60^{\circ}, m\angle C = 30^{\circ} \) (the third option)
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complete the proof that $\\triangle stu \\cong \\triangle rvu$. (image …
AAS (Angle - Angle - Side) Congruence Postulate
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each leg of a 45°-45°-90° triangle measures 14 cm. what is the length o…
\(14\sqrt{2}\) cm (Option: \(14\sqrt{2}\) cm)
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which rule explains why these triangles are congruent? image of triangl…
AAS
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which rule explains why these triangles are congruent? j k g f m h asa …
D. SAS (assuming the options are labeled as A. ASA, B. AAS, C. SSS, D. SAS, E. These triangles cannot be proven congruent. But based on the given options in the problem, if we con…
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which rule explains why these triangles are congruent? two triangles, x…
ASA
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practice makes better graph the image of a(0, -2), b(2, -2) and c(1, -5…
1. Final transformed points: $A'(2,2)$, $B'(4,2)$, $C'(3,5)$ 2. Final transformed points: $A'(-4,-5)$, $B'(-6,-5)$, $C'(-5,-8)$
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the cylinder and cone shown below have congruent bases and equal height…
s: (a) \( \boxed{126} \) (b) \( \boxed{42} \) (c) The value is \( \boxed{\frac{1}{3}} \), and the correct option is "This equation is true for all cylinders and cones with congrue…
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the cone and cylinder shown below have congruent bases and equal height…
s: (a) \( \boldsymbol{11} \) (b) \( \boldsymbol{33} \) (c) \( \boldsymbol{\frac{1}{3}} \); The correct option is: "This equation is true for all cylinders and cones with congruent…
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a buildings rafter forms the hypotenuse of a 30°-60°-90° triangle with …
4.5
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the cylinder and cone shown below have congruent bases and equal height…
\( 75 \) ### Part (b)
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consider the line $-x - 6y = -4$. what is the slope of a line parallel …
Slope of a parallel line: \(-\frac{1}{6}\) Slope of a perpendicular line: \(6\)
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amari is standing 50 feet from the base of a building. from where he st…
\(50\sqrt{3}\) ft (corresponding to the option " \(50\sqrt{3}\) ft")
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what is the measure of the largest angle of the triangle? 15 18?° 26 ro…
\( 103.62^\circ \)
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the length of segment ab is 9 mm. which statements regarding triangle a…
- \( \overline{AB} \) is the shortest segment in \( \triangle ABC \). (Correct) - \( \overline{AC} = 2AB \) (Correct)
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use pascals triangle to complete the expansion of ((v - w)^7). (v^7 - 7…
\(35v^{3}w^{4}\)
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use pascals triangle to complete the expansion of $(y - z)^4$. $y^4 + \…
The coefficient for \(y^{3}z\) is \(- 4\) (but if we follow the problem's form which has a plus sign, maybe there's a mistake, but if we consider the Pascal's Triangle coefficient…
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use pascals triangle to complete the expansion of (y - z)^5. y^5 + -5 y…
The missing exponent for \(z\) in the term \(-5y^{4}z^{\square}\) is \(1\), so the box should be filled with \(1\).
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use pascals triangle to complete the expansion of (q - r)^6. q^6 - 6q^5…
The coefficient is \(15\) and the exponent of \(r\) is \(4\), so the boxed coefficient is \(15\) and the boxed exponent of \(r\) is \(4\). So the term is \(15q^{2}r^{4}\), so the …
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find the sin 112.5° using the half-angle formula. rationalize the denom…
\(\sin112.5^{\circ}=\frac{\sqrt{2+\sqrt{2}}}{2}\) (So the values in the boxes are 2, 2, and 2 respectively)
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use pascals triangle to complete the expansion of $(p - q)^3$. $p^3 + \…
The coefficient of \(p^{2}q\) is \(-3\) and the coefficient of \(pq^{2}\) is \(3\). So the first box (for \(p^{2}q\)) is \(-3\) and the second box (for \(pq^{2}\)) is \(3\).
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use pascals triangle to complete the expansion of $(t + u)^7$. $t^7 + 7…
First blank: \(1\), Second blank: \(5\) So the completed terms are \(7t^{6}u^{1}\) and \(21t^{5}u^{2}\)
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use pascals triangle to complete the expansion of (s + t)^5. s^5 + 5s^4…
First blank: 2, Second blank: 1 So the filled terms are \(10s^{3}t^{2}\) and \(5s^{1}t^{4}\)
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use pascals triangle to complete the expansion of $(r + s)^4$. $r^4 + 4…
First blank: \(1\), Second blank: \(2\) (So the filled expansion is \(r^{4}+4r^{3}s^{1}+6r^{2}s^{2}+4rs^{3}+s^{4}\))
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use pascals triangle to complete the expansion of ((x + y)^3). (x^3 + 3…
\(3\)
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use pascals triangle to complete the expansion of (x + y)^6. x^6 + 6x^5…
15
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use pascals triangle to complete the expansion of $(v + w)^7$. $v^7 + 7…
35
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use pascals triangle to complete the expansion of $(r + s)^5$. $r^5 + 5…
10
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use pascals triangle to complete the expansion of $(t + u)^2$. $t^2 + \…
\(2\)
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use pascals triangle to complete the expansion of $(y + z)^4$. $y^4 + 4…
6
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which 30°-60°-90° triangle is labeled with the correct side length rati…
The second triangle (with angles \(30^\circ\), \(60^\circ\), right angle; sides \(1\), \(\sqrt{3}\), \(2\))
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given that $\\triangle abc$ is equilateral, and $\\overline{ad}$ bisect…
2
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given that △abc is equilateral, and \\(\\overline{ad}\\) bisects \\(\\a…
For the ratio part: The side lengths of \( \triangle ADB \) are in the ratio \( 1:\sqrt{3}:2 \) as shown above. For question 6, the answer is \( BD \), so \( 2(BD)=BC \).
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given that △abc is equilateral, and \\(\\overline{ad}\\) bisects \\(\\a…
CD
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given that △abc is equilateral, and \\(\\overline{ad}\\) bisects \\(\\a…
\( 90^\circ \)
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given that △abc is equilateral, and ad bisects ∠a, show that the side l…
isosceles
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given that △abc is equilateral, and overline{ad} bisects ∠a, show that …
\(30^{\circ}\)
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function 3 linear not linear function 4 linear not linear
s: - For Function 3: Not linear (circle the "Not linear" option) - For Function 4: Not linear (circle the "Not linear" option)
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given that △abc is equilateral, and \\(\\overline{ad}\\) bisects \\(\\a…
\(60^\circ\) (corresponding to the option with \(60^\circ\))
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for each function graphed below, determine whether it is linear. functi…
Not linear (select the "Not linear" option for Function 1) ### Function 2
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which of the following points most closely represents \\(\\sqrt{27}\\)?…
# Explicación: ## Paso1: Calcular cuadrados cercanos $5.1^2 = 26.01$, $5.2^2=27.04$, $5.3^2=28.09$ ## Paso2: Comparar con $\sqrt{27}$ $\sqrt{27} \approx 5.196$, que es muy cercano…
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what is the length of a leg of an isosceles right triangle whose hypote…
\( 3\sqrt{2} \) (corresponding to the option: \( 3\sqrt{2} \))
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determine whether each number is rational or irrational. | | rational |…
- \(\boldsymbol{\sqrt{98}}\): Irrational (select the circle under "Irrational") - \(\boldsymbol{\sqrt{25}}\): Rational (select the circle under "Rational") - \(\boldsymbol{\sqrt{1…
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the length of segment ef is 12 cm. which statements regarding triangle …
The correct statements are: - \( DF = 6\space cm\) - \( DE = 6\sqrt{3}\space cm\) - \( \overline{EF}\) is the longest side of \( \triangle DEF\)
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ce and fh are parallel lines. which angles are corresponding angles? ∠e…
$\angle EDB$ and $\angle HGD$ (o en símbolos $\angle EDB$ y $\angle HGD$)
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2. where should the linear inequality $y \\leq \\frac{1}{4}x - 3$ be sh…
B. Below the line
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588 in the diagram below of isosceles triangle ahe with the vertex angl…
2) \( \boldsymbol{\frac{AC}{EF}=\frac{AB}{ED}} \)
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g.srt.b.5: similarity 577 triangle jgr is similar to triangle mst. whic…
2) $\angle G \cong \angle T$
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10 ab and cd are parallel. give a reason why a and d are equal. give a …
\( a \) and \( d \) are equal because \( AB \parallel CD \) (given) and \( AC \) is a transversal; by the alternate interior angles theorem, alternate interior angles are equal. #…
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triangle rst is rotated 180° about the origin, and then translated up 3…
\(\boldsymbol{\triangle RST \cong \triangle ABC}\) (the option with \(\triangle RST \cong \triangle ABC\))
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termine $\\angle oac$ and $\\angle aoc$.
\( \angle OAC = 75^\circ \) and \( \angle AOC = 30^\circ \)
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determine $\\angle dba$.
$\boxed{33^\circ}$
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determine $\\angle dce$.
\( \angle DCE = 92^\circ \)
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name: 6) solve for the unknown angles. determine the value of x. (figur…
\(x = 8\)
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determine $\\angle cbd$.
\( \angle CBD = 47^\circ \)
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ab||ef and de||bc. determine ∠cqf. determine ∠cdb, if ∠acb is 41°.
\( \angle CQF = \boxed{141^\circ} \)
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ab||ef and de||bc. determine ∠cqf. determine ∠cdb, if ∠acb is 41°.
\( \boldsymbol{141^\circ} \)
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solve problems involving right triangles. determine the length of the u…
The length of the unknown side (hypotenuse) is 15 cm. ### Part b
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how many periods are shown in this graph? -2π 0 2π 4π
3
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step | statement | reason 1 | abcd is a parallelogram, \\(\\overline{ce…
The reason is "Both pairs of opposite sides are congruent (or: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram)" (more …
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question given: (abcd) is a parallelogram and (overline{ce} cong overli…
The reason for \(\overline{BC} \parallel \overline{AD}\) is "Opposite sides of a parallelogram are parallel". To fully prove \(FBED\) is a parallelogram, since \(\overline{BE} \co…
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given: abcd is a parallelogram and \\(\\overline{ce} \\cong \\overline{…
The reason for \( \overline{BE} \cong \overline{FD} \) is: If \( \overline{BC} \cong \overline{AD} \) and \( \overline{CE} \cong \overline{FA} \), then \( \overline{BC}+\overline{…
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given: abcd is a parallelogram and \\(\\overline{ce} \\cong \\overline{…
The reason for \( \overline{BE} \cong \overline{FD} \) is: If two congruent segments are added to two other congruent segments, the resulting segments are congruent (or "Addition …
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given: abcd is a parallelogram and \\(\\overline{ce} \\cong \\overline{…
The reason for \(\overline{BC} \cong \overline{AD}\) is "Opposite sides of a parallelogram are congruent".
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given: abcd is a rhombus and \\(\\overline{df}\\) bisects \\(\\overline…
The reason for step 9 is "Transitive Property of Congruence (If two segments are congruent to the same segment, then they are congruent to each other)" and we have proven \( \over…
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step statement reason 1 abcd is a rhombus \\(\\overline{df}\\) bisects …
All sides of a rhombus are congruent
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statement reason abcd is a rhombus given \\(\\overline{df}\\) bisects \…
The reason for \(\overline{BF}\cong\overline{DC}\) is "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)".
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step\tstatement\treason 1\tabcd is a rhombus \t\\overline{df} bisects \…
The reason for $\triangle DEC \cong \triangle FEB$ is "ASA (Angle - Side - Angle) congruence criterion" (or more precisely, "If two angles and the included side of one triangle ar…
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step 1: statement - abcd is a rhombus, \\(\\overline{df}\\) bisects \\(…
The reason for \( \angle C \cong \angle EBF \) is "Alternate Interior Angles are congruent (when two parallel lines are cut by a transversal)".
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question given: abcd is a rhombus and \\(\\overline{df}\\) bisects \\(\…
To prove \(\overline{BF}\cong\overline{AD}\): 1. **Properties of Rhombus**: In rhombus \(ABCD\), \(AD = BC\) (all sides of a rhombus are congruent) and \(DC\parallel AB\) (opposit…
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prove: $\\triangle gec \\cong \\triangle hfa$. step\tstatement\treason …
The reason for $\triangle GEC \cong \triangle HFA$ is the Angle - Angle - Side (AAS) Congruence Theorem.
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prove: $\\triangle gec \\cong \\triangle hfa$.\ step\\tstatement\\treas…
The reason for \(\overline{BC} \parallel \overline{AD}\) is "Opposite sides of a parallelogram are parallel" (or "Definition of a parallelogram").