Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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1.) triangles qrs and xyz are congruent. answer the following questions…
a. \(QR = XY\), \(RS = YZ\), \(QS=XZ\) b. \(\angle Q=\angle X\), \(\angle R=\angle Y\), \(\angle S=\angle Z\) c. \(x = 12\)
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what figure results from a horizontal cross section of a sphere? rectan…
Circle
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name 4. 12 cm 10 cm 6 cm 8 cm a. 36 cm² b. 60 cm² c. 24 cm² d. 40 cm²
B. \(60\space cm^{2}\)
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what figure results from a horizontal cross section of a sphere? rectan…
Circle
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a hollow post is made out of a lightweight aluminum alloy that is 1.5 c…
\(1710\) \(cm^{3}\)
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6 describe, in coordinate notation, the following sequence of transform…
\((y, -x)\)
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a wedding tent is built in the shape of a right rectangular prism toppe…
\(5113.7\) cubic feet.
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5 what 2 vocabulary terms describe when a pre - image is mapped onto an…
Congruent, Rigid motions
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use structure on a separate sheet of paper, draw a right triangle abc a…
\(270^{\circ}\)
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electric utility poles in the form of right cylinders are made out of w…
\(\$530.14\)
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triangle abc is transformed to create triangle def. what sequence of tr…
Translate 2 units to the right, then reflect over the x - axis.
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under a rotation about the origin, ( a(5,-1) ) is mapped to the point (…
\(B'(-6,-4)\) The rotation maps \((x,y)\) to \((-y,x)\), so it is a \(90^{\circ}\) counter - clockwise or \(270^{\circ}\) clockwise rotation. Therefore, the image of \((-4,6)\) is…
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1 analyze parallelogram defg. if you rotate the parallelogram about the…
\((5,-6)\)
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an aquarium can be modeled as a right rectangular prism and it can hold…
\(20\)
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lesson 8 practice problems 1 the picture shows a circle divided into 12…
The area of the paper - plate is approximately \(63.585\) square inches. The area of the circular table is approximately \(1074.665\) square inches.
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hiking a damaged compass points northwest instead of north. if you trav…
135, 225
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8. who famously saved a portrait of george washington when england burn…
8. a. Dolly Madison 9. c. "The Era of Good Feelings" 10. c. Sphere of Influence Bonus: Thomas Jefferson
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the line segment xy with endpoints x(3,1) and y(2, - 2) is rotated such…
\((x,y)\to(-x,-y)\)
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multiple choice: circle the correct answer. each 1 pt. 1. a time period…
B. Grace period
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parallelogram jklm has vertices ( j(2,1) ), ( k(7,1) ), ( l(6,-3) ), an…
\((x,y)\to(y,-x)\) (a \(270^{\circ}\) counter - clockwise rotation about the origin or a \(90^{\circ}\) clockwise rotation about the origin)
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you want to find the treasure located on the map at x. you are located …
Reflect in the \(y\) - axis, then rotate \(90^{\circ}\) counter - clockwise about the origin, then translate \(1\) unit right and \(1\) unit up.
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28. reasoning a trapezoid has vertices ( a(-6,-2), b(-3,-2), c(-1,-4) )…
a. \(A'(6,2)\), \(B'(3,2)\), \(C'(1,4)\), \(D'(6,4)\) b. Reflect the trapezoid over the \(y\) - axis and then over the \(x\) - axis.
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the angle measures in a triangle are in the ratio 1:3:5. the longest si…
11.1 in
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caleb and emily are standing 100 yards from each other. caleb looks up …
63.4 yd
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what is one possible solution for the triangle below? yz ≈ 43.0, m∠x ≈ …
\(YZ\approx19.3,m\angle X\approx85.4^{\circ},m\angle Z\approx26.8^{\circ}\)
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based on the sketch below, how far is joeys house from the park? school…
\(0.86\) mi.
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jake and maddie each take the closest path from their homes to the stor…
5.9 m
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Question was provided via image upload.
\(x = 28\)
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convert the following angle from degrees to radians. express your answe…
$\frac{5\pi}{6}$
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convert the angle 1 radian to degrees, rounding to the nearest 10th.
57.3
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convert the angle 6 radians to degrees, rounding to the nearest 10th.
$343.8$
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convert the angle \\( \\frac { 5 \\pi } { 4 } \\) radians to degrees.
225
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from where kiana is standing, she must look up at a 50° angle to see th…
\(141.8\space ft\)
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convert the following angle from degrees to radians. express your answe…
$\frac{\pi}{6}$
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convert the following angle from degrees to radians. express your answe…
$\frac{17\pi}{12}$
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from where kiana is standing, she must look up at a 50° angle to see th…
The height of the building is approximately \(142\) feet.
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jamal draws triangle xyz. if ( mangle x = 46^{circ}), ( xz = 10), and (…
3.4 or 10.4
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convert the angle $\\frac{7\\pi}{6}$ radians to degrees. answer submit …
\(210\)
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triangle mnp has vertices n(2,2) and p(0,-2). the triangle is symmetric…
\(63.6^{\circ}\)
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the bottom of a 12 - foot ladder is placed on the ground 7 feet from th…
\(35.7^{\circ}\)
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7 a square garden has an area of 400 square feet. what is the length of…
7. The length of each side of the square garden is \(20\) feet and \(80\) feet of fencing is needed. 8. The possible pairs of base and height for the triangle (where \(b\) is the …
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1 ( h ) is the midpoint of ( overline{g i} ) given 2 ( overline{i k} co…
Statement: \(\triangle GHJ\cong\triangle IHK\); Reason: SSS Congruence Theorem.
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w is the midpoint of \\( \\overline { v x } \\), \\( \\overline { x z }…
1. Given 2. Given 3. Given 4. Definition of midpoint 5. SSS (Side - Side - Side) Congruence Theorem
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41) \\( \\overleftrightarrow { q t } \\) bisects \\( \\angle r q s \\).…
$\triangle QST\cong\triangle QRT$ (by SAS congruence criterion)
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41) z is the midpoint of \\( \\overline { v x } \\) and \\( \\overline …
1. Given 2. Given 3. Definition of midpoint 4. Definition of midpoint 5. Vertical angles theorem 6. SAS (Side - Angle - Side) congruence criterion
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complete the proof that ( \triangle qtucong\triangle rsu ). 1 ( overlin…
1. Given 2. Given 3. Vertical Angles Theorem 4. SAS (Side - Angle - Side)
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1 (\triangle fph) is equilateral given 2 (overline{fg}congoverline{ei})…
4. Sides of an equilateral triangle are equal; 5. \(SAS\) (Side - Angle - Side) congruence criterion.
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wx || yz. complete the proof that δw 1 wx || yz 2 wx ≅ yz 3 ∠wyz ≅ ∠xwy…
\(\triangle WYZ\cong\triangle YWX\) (by the SAS congruence criterion)
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wx || yz. complete the proof that △wyz ≅ △ywx. statement 1 wx || yz 2 w…
\(\triangle WYZ\cong\triangle YWX\) (by SAS congruence criterion)
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wx || yz. complete the proof that △wyz ≅ △ywx. statement 1 wx || yz 2 w…
\(\triangle WYZ\cong\triangle YWX\) (by the SAS congruence criterion)
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wx || yz. complete the proof that △wyz ≅ △ywx. statement 1 wx || yz 2 w…
\(\triangle WYZ\cong\triangle YWX\) (by SAS congruence criterion)
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complete the proof that ( \triangle hjk cong \triangle jhi ).
1. Given 2. Given 3. Reflexive Property of Congruence 4. SSS (Side - Side - Side) Congruence Criterion
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tw bisects ∠utv. complete the proof that △tvw ≅ △tuw. 1 tw bisects ∠utv…
1. Given; 2. Given; 3. Definition of angle bisector; 4. Reflexive property of congruence; 5. SAS (Side - Angle - Side) congruence criterion.
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t is the midpoint of su. complete the proof that \\( \\triangle tuw \\c…
4. Reason: Definition of midpoint 5. Reason: SSS (Side - Side - Side) Congruence Criterion
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cool down! write a congruence statement for each pair of congruent figu…
\(\text{LMNOP}\cong\text{AYHFS}\), \(\text{DEFC}\cong\text{XUVW}\), \(\text{OMN}\cong\text{TEU}\)
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i is the midpoint of \\( \\overline{g h} \\) and \\( \\overline{f i} \\…
\(\triangle FGI\cong\triangle FHI\) by the \(SAS\) (Side - Angle - Side) congruence criterion.
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1 z is the midpoint of \\( \\overline { w y } \\) given 2 z is the midp…
3. Definition of mid - point; 6. SAS (Side - Angle - Side) congruence criterion.
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3. quadrilateral pqrs is a rotation of polygon vzyw. is angle qrs congr…
NO! The angle congruent to \(\angle QRS\) is \(\angle VZW\)
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1 j is the midpoint of \\( \\overline { f h } \\) given 2 j is the midp…
4. Definition of midpoint; 6. SAS (Side - Angle - Side) congruence criterion.
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geometry the volume of a pyramid is given by the formula $v = \\frac{bh…
6
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2. polygon hijkl is a reflection and translation of polygon gfonm. is s…
NO! The segment that is congruent to segment \(NM\) is segment \(KL\).
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sv ≅ rv and tv ≅ uv. complete the proof that △stv ≅ △ruv. 1 sv ≅ rv giv…
Vertical Angles Theorem
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activity 2: are these parts congruent? here is a diagram with two trian…
NO. The angle that is congruent to \(\angle ADB\) is \(\angle CBD\).
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complete the proof that ( \triangle vwx cong \triangle vyx ).
By the SSS (Side - Side - Side) Congruence Criterion.
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activity 1: which triangles are congruent? here are 3 triangles. 1. tri…
1. Triangle \(PQR\) is congruent to triangle \(NML\) because of the SAS (Side - Angle - Side) congruence criterion. 2. First, rotate triangle \(PQR\) to match the angle orientatio…
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ce area of an object would be useful. umingehicleshow all of your think…
Volume: \(576\) Surface area: \(624\)
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activity 1: which triangles are congruent? here are 3 triangles. 1. tri…
Triangle \(PQR\) is congruent to triangle \(NML\) by the SAS (Side - Angle - Side) congruence criterion.
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5. triangle was rotated 90 degrees counterclockwise followed by a refle…
\(y=-x\)
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a sequence of transformations maps triangle qrs onto congruent triangle…
A. a reflection across the x - axis, followed by a 90 - degree clockwise rotation about the origin. B. a 180 - degree clockwise rotation about the origin, followed by a reflection…
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the converse of the parallelogram side theorem given: \\( \\overline { …
LMNO is a parallelogram.
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give the center and radius of the circle. $x^{2}+y^{2}=25$ center: radi…
Center: \((0,0)\) Radius: \(5\)
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give the center and radius of the circle. $x^{2}+(y - 4)^{2}=9$ center:…
Center: \((0,4)\) Radius: \(3\)
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give the center and radius of the circle. $(x + 1)^{2}+(y - 1)^{2}=4$ c…
Center: \((-1,1)\) Radius: \(2\)
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find the center and the radius of the circle. $x^{2}+y^{2}+4x + 6y-36 =…
Center: \((-2,-3)\) Radius: \(7\)
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give the center and radius of the circle. $(x - 5)^{2}+y^{2}=16$ center…
Center: \((5,0)\) Radius: \(4\)
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write the standard equation of the circle with center:$(-11,-8)$ radius…
\((x + 11)^2+(y + 8)^2=16\)
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question given: \\( \\overline { e f } \\parallel \\overline { g h } \\…
\(\angle GJI\cong\angle LKF\) is proved as above.
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∠dab is a right angle and ∠abc is a right angle. prove: ∠acb ≅ ∠dac. no…
Since \(\angle ACB\) and \(\angle DAC\) both equal \(90^{\circ}-\angle BAC\), we can conclude that \(\angle ACB\cong\angle DAC\) (by the definition of congruent angles: angles wit…
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read the sentences below, filling in the blanks with items from this li…
1. SAS 2. congruent 3. sides 4. proportional 5. 180 6. vertex 7. similarity 8. similar
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5. ( 2(x + 14)+(2x - 14)= ) ( 4x + 14 ) ( \frac{+2x}{4x+14} ) ( \frac{1…
\(-x + 2\)
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given: jm bisects ∠j. jm ⊥ kl prove: △jmk ≅ △jml
\(\triangle JMK\cong\triangle JML\) (by AAS congruence criterion)
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given: ∠b and ∠d are right angles. overline{ae} bisects overline{bd} pr…
$\triangle ABC\cong\triangle EDC$
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given: ∠k ≅ ∠m, l is midpoint of km prove: l is midpoint of jp 5)
$L$ is the mid - point of $\overline{JP}$ is proved as above.
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given: wx || yz, wz ≅ wx, yz ≅ yz prove: △wxz ≅ △yzx
\(\triangle WXZ\cong\triangle YZX\) is proved by the Side - Angle - Side (SAS) congruence criterion.
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given: \\( \\overline{ya} \\cong \\overline{ba} \\), \\( \\angle b \\co…
By using the vertical - angles theorem and the SAS congruence criterion, we have proved that $BC\cong YZ$.
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more triangle congruence proofs for each problem write either a 2 - col…
$\triangle ABC\cong\triangle EDC$ (by AAS congruence criterion: $\angle ABC\cong\angle EDC$, $\angle ACB\cong\angle ECD$, $\overline{BC}\cong\overline{DC}$)
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a30 name: _ more triangle congruence proofs for each problem write eith…
\(\angle A\cong\angle E\) is proved as shown above.
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name: lesson 8:more triangle congruence proofs cool down: write a flow …
$\angle T\cong\angle W$ is proved as above.
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add. use models if needed. (examples 1 - 5) 1. $(4x + 8)+(7x + 3)=$ 2. …
\(11x + 11\)
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answer the question in this part. each correct answer will receive 4 cr…
The perimeter of the rectangle as a trinomial is \(2x^{2}+14x + 4\). The area of the rectangle as a trinomial is \(4x^{3}+12x^{2}+8x\)
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which triangle is different to the others?
The triangle \(\triangle MLN\) is different from the others.
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without any given or any markings, by just looking at the picture, what…
\(\angle AED\cong\angle BEC\)
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reflexive property what segment do the two triangles share? af ae fe fc…
For the first question: \(FE\) For the second question: \(\overline{FE}\cong\overline{FE}\)
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reflexive property what segment do the two triangles share? af ae fe fc…
FE
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practice 7 (from unit 2, lesson 10) here is figure abcd. \\( \\overline…
Se ha demostrado que \(AD\cong BC\)
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practice 6 (from unit 3, lesson 1) polygon q is a scaled copy of polygo…
A. \( \frac{3}{4} \)
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a polygon has perimeter of 12 units. it is dilated with a scale factor …
A. 9 units
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practice 1 pentagon abcde is the image of pentagon abcde after a dilati…
\(\frac{5}{3}\)
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find the length of the third side. if necessary, round to the nearest t…
\(24\)
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find the length of the third side. if necessary, round to the nearest t…
\(3\)