Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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line segment su is dilated to create su using point q as the center of …
\(2\)
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details no additional details were added for this assignment. 5. ( over…
6. \(\triangle AXP\cong\triangle BXP\) 7. \(\overline{PA}\cong\overline{PB}\)
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marcello is constructing the perpendicular bisector of \\( \\overline {…
Use the straightedge to draw a line through points \(X\) and \(Y\)
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in the figure below, lines ( l ) and ( k ) are parallel. suppose that (…
By the angle addition property, \(m\angle4 + m\angle2 + m\angle5 = 180^{\circ}\). We are given that \(m\angle4 = 43^{\circ}\) and \(m\angle5 = 72^{\circ}\), so \(m\angle2 = 65^{\c…
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7. $(5x - 7)^{circ}$ $(8x - 55)^{circ}$
\(x = 16\)
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in the diagram. \\( \\angle q \\cong \\angle x \\). what additional inf…
side \(r\cong\) side \(z\) and side \(s\cong\) side \(y\)
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the proof that ( \triangle efg cong \triangle jhg ) is shown. given: ( …
\(\angle GFE\cong\angle GHJ\)
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is △wxz ≅ △yzx? why or why not? no, there is only one set of congruent …
Yes, they are congruent by SAS.
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the proof that ( \triangle mnscong\triangle qns ) is shown. select the …
MS and QS
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if vx = wz = 40 cm and m∠zvx = m∠xwz = 22°, can △vzx and △wxz be proven…
C. Yes, along with the given information, \(\overline{ZX}\cong\overline{ZX}\) by the reflexive property.
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the proof that ( \triangle acbcong\triangle ecd ) is shown. given: ( ov…
$\angle ACB\cong\angle ECD$
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triangle congruence: sas triangles rqs and ntv have the following chara…
No, it is necessary to know that another set of corresponding sides is congruent.
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triangle congruence: sas how can a translation and a rotation be used t…
Translate \(H\) to \(L\) and rotate about \(H\) until \( \overline{HK}\) lies on the line containing \( \overline{LM}\).
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two rigid transformations are used to map \\( \\triangle hjk \\) to \\(…
a rotation about point \(H\)
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triangle congruence: sas in the diagram, \\( \\overline { k l } \\cong …
\(\angle L\cong\angle R\)
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which rigid transformation would map △aqr to △akp? a reflection across …
a rotation about point \( A \)
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how can △wxy be mapped to △mnq? translate vertex w to vertex m, then re…
\(\overline{XY}\)
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given: \\( \\triangle dfe \\) is isosceles with base \\( \\overline{fe}…
The first blank is filled with "it is given" (as per the problem's given conditions). The second blank is \(\overline{DF}\) (since in an isosceles triangle \(\triangle DFE\) with …
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analyze the figure and the two - column proof which statement/reason pa…
$\triangle AFC\cong\triangle DEB$; Hypotenuse - Leg Congruence Theorem
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given ∠tuw ≅ ∠srw, rs ≅ tu prove ∠rst ≅ ∠uts complete the paragraph pro…
First blank: \( SSS \) (Side - Side - Side congruence criterion). Second blank: \( CPCTC \) (Corresponding Parts of Congruent Triangles are Congruent).
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the reason in proving congruent triangles rt || sp, rq ≅ qp, rp bisects…
vertical angles theorem
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given \\( \\overline { a b } \\cong \\overline { a e } \\), \\( b c \\c…
1. \(SAS\) (Side - Angle - Side) 2. \(AD\)
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oving triangles congruent given: c is the midpoint of ( overline{bd} ).…
2. Reason: definition of midpoint; 5. Statement: \( \angle BCA\cong\angle DCA \)
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in the figure below wu ≅ vt the congruency theorem can be used to prov …
C. SAS
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proving triangles congruent given: c is the midpoint of \\( \\overline{…
2. Reason: definition of midpoint; 5. Statement: \( \angle BCA\cong\angle DCA \)
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which congruency theorem can be used to prove that \\( \\triangle abd \…
C. SAS
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the frame of a bridge is constructed of triangles as shown. what additi…
\(m\angle STU = 37^{\circ}\) and \(m\angle VTU = 37^{\circ}\); \(UV = 14\mathrm{ft}\) and \(m\angle TUV = 45^{\circ}\)
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consider \\( \\triangle wxy \\) and \\( \\triangle bcd \\) with \\( \\a…
no, because the corresponding congruent angles listed are not the included angles
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etermining a combination of rigid transformations how can △abc be mappe…
First, translate vertex \(A\) to vertex \(X\). Next, rotate \(\triangle ABC\) to align the sides and angles.
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triangle congruence: sas identifying additional information needed to p…
\(\angle DFE\cong\angle DFG\)
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identifying rigid transformations which rigid transformations would map…
a rotation and a reflection, a translation and a reflection
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a. sector area = radius × central angle (in degrees) b. sector area = 2…
- For the sector area formula: c. \(SectorArea=0.5\times Radius^{2}\times CentralAngle\) (in radians) - For the arc - length formula: b. \(ArcLength = Radius\times CentralAngle\) …
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if a central angle measures 2π/5 radians in a circle with radius 5 cm, …
For the arc - length problem: a. \(2\pi\mathrm{cm}\) For the radians - in - a - quarter - circle problem: c. \(\frac{\pi}{2}\) radians
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what is the area of a sector formed by a central angle of π/3 radians i…
b. \(6\pi\space square\space cm\)
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which of the following is a valid method for calculating the sector are…
For the formula question: B. \(Sector\ Area = 0.5\times Radius^{2}\times Central\ Angle\ (in\ radians)\) For the unit question: B. Square centimeters
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choose the expression that correctly represents the conversion of degre…
For the conversion formula: B. Radians \(=\frac{\text{Degrees}\times\pi}{180}\) For the central - angle problem: B. \(\pi\) radians
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the triangles shown are congruent by the sss congruence theorem the dia…
rotation, then reflection, then translation
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triangle abc is congruent to △abc by the hl theorem what single rigid t…
B. reflection
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the triangles are congruent by sss or hl which transformation(s) can ma…
reflection only
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point h is the midpoint of side fk for the triangles to be congruent by…
\(6\)
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the triangles are congruent by the sss congruence theorem which transfo…
translation, then reflection
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for the triangles to be congruent by hl, what must be the value of x? 2…
B. 3
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which explains whether \\( \\triangle fgh \\) is congruent to \\( \\tri…
They are not congruent because only two pairs of corresponding sides are congruent
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which value of x would make △suv ≅ △tuw by hl? 2 3 4 5
\(3\)
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the two triangles created by the diagonal of the parallelogram are cong…
reflection
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the four - sided geometric figure pictured is called a parallelogram. o…
B. The triangles can be proven congruent using SSS
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the triangles are congruent by the sss congruence theorem which transfo…
reflection then translation
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isosceles triangle abc is folded along bm with m chosen in such a way t…
- First question: AM and CM - Second question: BM and BM - Third question: AB and CB
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m is the midpoint of ad what single transformation is required to map o…
Reflection
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23. which of the following is an example of a correct proportion for si…
d. \(AB/DE = AC/DF\)
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m is the midpoint of ad what value of x will make triangles abm and dcm…
C. 7
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in the diagram bc ef and ∠a and ∠d are right angles for the triangles t…
C. 17
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practice using the sss and hl congruence theorems. triangle def and tri…
\(\overline{DE}\cong\overline{DG}\) (i.e., the third option)
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11. what is the included angle between sides ab and ac in △abc? a. ∠bca…
d. \(\angle BAC\)
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8. triangle pqr has sides pq = 9, pr = 12, and qr = 15. for triangle xy…
b. \(XY = 9\), \(XZ = 12\), \(YZ = 15\)
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4. what is the ratio of the corresponding sides \\( \\frac { a b } { d …
\(\frac{AB}{DE}=2\) and \(\frac{AC}{DF}=2\)
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the sss proof used the rigid transformations illustrated here. which tr…
rotation, then reflection, then translation
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determine the rigid transformations that will map \\( \\triangle a b c …
Translate vertex X to vertex A, rotate \( \triangle XYZ \) to align the sides and angles.
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determine the rigid transformations that will map (\triangle abc) to (\…
C. Reflect \( \triangle ABC \) across side \( AB \), translate vertex \( C \) to vertex \( X \)
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given prove it is given that angle lno is congruent to angle and angle …
1. $\angle LNM$ 2. $\angle LMN$ 3. reflexive property 4. ASA (Angle - Side - Angle)
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are the triangles congruent? if so, how do you know? yes, because all t…
not enough information given
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during geometry class, students are told that \\( \\triangle tsr \\cong…
Sam is correct.
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extra practice level up your skills! mixed proofs 3. helicopter pad a l…
\(m\angle2 = 137^{\circ}\)
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3. helicopter pad a local hospital builds a new helicopter pad as shown…
\(112^{\circ}\)
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extra practice level up your skills! mixed proofs 3. helicopter pad a l…
\(m\angle2 = 112^{\circ}\)
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k extra practice level up your skills! mixed proofs find the measure of…
1. \(m\angle RPN = 55^{\circ}\) 2. \(m\angle LPN=135^{\circ}\)
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extra practice level up your skills! mixed proofs proof write the corre…
| Statements | Reasons | |--|--| | 1. \(\overline{MP}\cong\overline{LP}\), \(\overline{LN}\cong\overline{MO}\) | 1. Given | | 2. \(MP = LP\), \(LN = MO\) | 2. Definition of \(\con…
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1 practice 1 here are triangles abc and def. what is the length of segm…
\(13.5\)
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can you conclude that triangle ghf is congruent to triangle gjk? explai…
yes, by AAS
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match the measureable quantity given by its formula with the appropriat…
speed = distance/time → meters per second area = (length)(width) → square meters volume = (length)(width)(height) → cubic centimeters perimeter = 2 (length) + 2 (width) → meters
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proof in the figure at the right, u is the midpoint of \\( \\overline{t…
Because \(U\) is the midpoint of \(\overline{TV}\), we know that \(TU = UV\). Substituting \(x = 3\), we find \(TU=9\) and \(UV = 9\). Next, we can find the lengths of \(UV\) and …
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what additional information could be used to prove that \\( \triangle x…
A. \(\angle Z\cong\angle G\) and \(\overline{XZ}\cong\overline{FG}\), B. \(\angle Z\cong\angle G\) and \(\angle Y\cong\angle E\)
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7 practice 7 (from unit 3, lesson 5) here is a diagram with triangles a…
B. Angle \(ACB\) is \(x^{\circ}\). C. Triangle \(ACB\) is similar to triangle \(ADE\).
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which graph shows the solution set of the inequality 2.9(x + 8) < 26.1?
The graph with an open - circle at \(x = 1\) and shading to the left.
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3 practice 3 which pair of polygons is similar? a b c d how did i do?
C.
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practice 2 which statement provides a valid justification for why all c…
D. I can translate the center of any circle to the center of another, and then dilate from that center by an appropriate scale factor, so they must be similar.
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which graph represents the solution set of the inequality ( x + 2 geq 6…
The third graph (the one with a closed - circle at \(4\) and an arrow extending to the right) represents the solution set of the inequality \(x + 2\geq6\).
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life lesson: your friends equal your future the phrase show me your fri…
B. career pursuits, relocations, and personal growth
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life lesson: your friends equal your future the phrase \show me your fr…
the impact of friends on personal development
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life lesson: your friends equal your future what is the core of the lif…
It emphasizes the importance of assessing friends' goals and attitudes.
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what additional information could be used to prove \\( \\triangle efg \…
- EG = 12 and E'G' = 12 - m∠G = 42° and m∠G' = 42° - \(\overline{EG}\cong\overline{E'G'}\)
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what additional information would be needed to prove that the triangles…
$\angle LNO \cong \angle LNM$
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is there a rigid transformation that maps triangle abc to triangle abd?…
C. yes, because a reflection across \(\overline{BA}\) will map \(\triangle ABC\) to \(\triangle ABD\)
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name all the angles that have ( v ) as a vertex. 13) 14) 15) 16) 17) 18…
Because if \(\angle ABC\) is acute (\(<90^{\circ}\)) and \(\angle DBE\) is obtuse (\(>90^{\circ}\)), having both \(D\) and \(E\) inside \(\angle ABC\) would make \(\angle DBE\) (f…
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two rigid transformations are used to map △hjk to △lmn. the first is a …
a rotation about point \(K\)
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how can \\( \\triangle wxy \\) be mapped to \\( \\triangle mnq \\)? tra…
\(\overline{WY}\)
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first determine if the triangles are similar. then find a and b.
The triangles are similar. \(a = \frac{112}{15}\approx7.47\) and \(b=\frac{128}{15}\approx8.53\)
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how can a translation and a rotation be used to map \\( \\triangle h j …
Translate \( K \) to \( N \) and rotate about \( K \) until \( \overline{HK} \) lies on the line containing \( \overline{LN} \)
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select the passage that has a more informative tone. the \standing - si…
The first passage (about the "standing - sitting dive") has a more informative tone.
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consider ( \triangle wxy ) and ( \triangle bcd ) with ( angle xcongangl…
no, because the corresponding congruent angles listed are not the included angles
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# 16 what is the most specific name for the quadrilateral below?
Parallelogram
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#17 what is the most specific name for the quadrilateral below?
Trapezoid
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given \\( \\triangle dfe \\) is isosceles with base \\( \\overline{fe},…
1. Given 2. \(DE\) 3. \(\angle DFC\) and \(\angle DEB\) 4. \(DFB\) and \(DEC\)
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given \\( \\overline { r t } \\parallel \\overline { s p }, \\overline …
vertical angles theorem
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given c is the midpoint of bd prove \\( \\triangle a c b \\cong \\trian…
2. Definition of midpoint 5. \(\angle BCA\cong\angle DCA\)
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can \\( \\triangle tsr \\) and \\( \\triangle qrs \\) be proven congrue…
yes, because along with the given information on the diagram, \(\overline{SR}\cong\overline{RS}\) by the reflexive property
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can \\( \\triangle tsr \\) and \\( \\triangle qrs \\) be proven congrue…
yes, because along with the given information on the diagram, \(\overline{SR}\cong\overline{RS}\) by the reflexive property
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how can \\( \\triangle abc \\) be mapped to \\( \\triangle xyz \\)? fir…
First, translate vertex \(A\) to vertex \(X\). Next, rotate \(\triangle ABC\) to align the sides and angles.
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to prove that \\( \\triangle def \\cong \\triangle dgf \\) by sas, what…
$\angle DFE\cong\angle DFG$
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which rigid transformations would map \\( \\triangle jkl \\) onto \\( \…
- a rotation and a reflection - a translation and a reflection - a translation only