Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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directions: use the figure and information to set create a formal proof…
1. \(\angle M\cong\angle P\) (Reason: Alternate Interior Angles Theorem) 2. \(PQ\cong NM\) (Reason: Given) 3. \(\angle N\cong\angle Q\) (Reason: Alternate Interior Angles Theorem)…
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write the coordinates of the vertices after a translation 2 units left …
\(Q'(-1,-2)\), \(R'(4,-2)\), \(S'(4,2)\), \(T'(-1,2)\)
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directions: for each triangle pair drawn, write the parts and pieces yo…
\(\angle F\cong\angle X\), \(\angle G\cong\angle Y\), \(\overline{HF}\cong\overline{ZX}\); The triangles are congruent, by ASA (Angle - Side - Angle), so \(\triangle FGH\cong\tria…
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question what is the image of $(6,12)$ after a dilation by a scale fact…
\((3,6)\)
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question what is the image of (0, -4) after a dilation by a scale facto…
\((0,-1)\)
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(score for question 1: ___ of 6 points) 1. write a paragraph proof for …
Since \( \overline{QS}\) bisects \( \angle PQR\), \( \angle PQS=\angle SQR\). Given \( m\angle PQS = 45^{\circ}\), then \( m\angle SQR = 45^{\circ}\). By the angle - addition post…
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what is the image of $(-9,3)$ after a dilation by a scale factor of $\f…
\((-3,1)\)
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write the coordinates of the vertices after a dilation with a scale fac…
\(E'(-2,-2)\), \(F'(2,-2)\), \(G'(1,2)\), \(H'(0,2)\)
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what is the image of (8, -8) after a dilation by a scale factor of 1/4 …
\((2,-2)\)
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directions: for each triangle pair drawn, write the parts and pieces yo…
\(\boxed{\angle G\cong\angle Y}\), \(\boxed{\angle F\cong\angle X}\), \(\boxed{\text{are}}\), \(\boxed{\text{AAS}}\), \(\boxed{XZY}\)
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10. p (2, 3), q (0, 2), r (-1, -2) rotation 90 degrees clockwise around…
\(P'=(3,-2)\), \(Q'=(2,0)\), \(R'=(-2,1)\), \(P''=(-3,-2)\), \(Q''=(-2,0)\), \(R''=(2,1)\)
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given ( m parallel n ), find the value of ( x ). answer attempt 1 out o…
$x = 40$
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given ( m parallel n ), find the value of ( x ). answer attempt 1 out o…
\(x = 11\)
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answer 1. \\( \\angle 2 \\cong \\angle 4 \\) 1. given 2. \\( m \\angle …
5. Definition of supplementary angles 7. Transitive property of equality 8. Substitution property of equality 9. Subtraction property of equality 10. Angle congruence postulate
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use the given information to prove that ∠6 ≅ ∠1. you are not allowed to…
\(\angle 6\cong\angle 1\) (by vertical - angles theorem and transitive property of congruence)
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2. make a table representing the relationship between the length of the…
The table is as shown above and the pattern in the table (\(P = 4s\)) is consistent with the physical interpretation of perimeter as the sum of the lengths of all four sides of a …
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directions: use the figure and information to set create a formal proof…
| Statement | Reason | |--|--| | \(AB\cong CB\) | Given | | \(AD\cong DC\) | Given | | \(BD\cong BD\) | Reflexive Property of Congruence | | \(\triangle ABD\cong\triangle CBD\) | …
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given ( mparallel n ), find the value of x. answer attempt 1 out of 2 (…
\(5\)
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the vertices are ( k(5,5) ). ( l(6,2) ). th of ( overline{lm} ) ? use t…
\(\sqrt{10}\)
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1. write a paragraph proof for the following conjecture given: \\( \\ov…
Since \( \overline{QS} \) bisects \( \angle PQR \), \( \angle PQS=\angle SQR \). Given \( m\angle PQS = 45^{\circ} \), then \( m\angle SQR = 45^{\circ} \). By the angle - addition…
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in $\\triangle klm$, the coordinates of the vertices are $k(5,5)$, $l(6…
The length of \(\overline{LM}\) is \(2\sqrt{10}\approx6.32\)
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directions: use the figure and information to set create a formal proof…
| Statement | Reason | |--|--| | \(AB\cong CB\) | Given | | \(AD\cong DC\) | Given | | \(BD\cong BD\) | Reflexive Property | | \(\triangle ABD\cong\triangle CBD\) | SSS (\(AB\cong…
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directions answer the question below to check your understanding and mo…
\(\sqrt{(-4 - 9)^2+(-6 - 8)^2}\)
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if the aas congruence theorem is to be used to show these two triangles…
\(\angle C\cong\angle Z\) because for AAS (Angle - Angle - Side) we need two angles and a non - included side. Here, if \(\angle C\cong\angle Z\), along with the given \(\angle B\…
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you have been given three corresponding parts of two congruent triangle…
a. \(\triangle JLH\cong\triangle FEG\) by SAS b. \(\triangle DYX\cong\triangle CMP\) by ASA
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describe a congruence transformation that maps the blue figure to the r…
4
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describe a congruence transformation that maps the blue figure to the r…
3
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describe a congruence transformation that maps the blue figure to the r…
4
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points q, p, and e form a triangle. the following relationships are als…
\(\triangle QPE\cong\triangle TRG\) by the SSS congruence theorem.
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points a, b, and c form a triangle. the following relationships are als…
\(\triangle ABC\cong\triangle DFE\) by the \(SSS\) congruence theorem.
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question 15 not necessarily drawn to scale: given: ab // de and ab = ed…
Vertical Angles
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the flower bed problem anthony chens family operates a full - service p…
The fourth model is a \(4\times4\) square of tiles (16 tiles arranged in 4 rows and 4 columns) and the fifth model is a \(5\times5\) square of tiles (25 tiles arranged in 5 rows a…
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complete the sentences describing the banquet hall. the perimeter of th…
2,256
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2. what is the hypothesis of the following conditional statement? condi…
B. A triangle has three congruent sides.
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conditional and bi - conditional statements quiz geometry a (fa25) co 3…
If I finish my chores, then I will go to the park.
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4. an informal proof uses ______________ to show that a conjecture is t…
C. specific examples
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1. which of the following does not belong in the second column of a for…
statements
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the flower bed problem anthony chens family operates a full - service p…
1. The next two models (for \(n = 4\) and \(n = 5\)) are squares made up of \(16\) (\(4\times4\)) and \(25\) (\(5\times5\)) tiles respectively. 2. The table has a linear relations…
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lines (ell), (m), and (n) are parallel and cut by transversal (p). ente…
The value of \(x\) is \(26\) and the value of \(y\) is \(36\).
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7. solve for the value of x and determine the measure of each angle x =…
\(x = 29\), \(m\angle A=87^{\circ}\), \(m\angle B=59^{\circ}\), \(m\angle C=34^{\circ}\)
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6. find the value of x that makes the triangles similar. show your work…
a. \(x = 4\) b. \(x = 14\)
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what is the scale factor of the dilation of triangle def? 3/10 3/7 7/3 7
\(\frac{3}{7}\)
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points q and r are midpoints of the sides of triangle abc. what is aq? …
\(20\) units
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which value of x would make (overline{fg}paralleloverline{bc})? 1 3 6 9
\(9\)
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to prove that \\( \\triangle aed \\sim \\triangle acb \\) by sas, jose …
\(\angle A=\angle A\)
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what is the length of (overline{mn})? 58 cm 75 cm 88 cm 116 cm
58 cm
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4 - 8 congruence in right triangles why do we not use a leg - leg (ll) …
D. This case is already covered by the SAS Postulate.
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4 - 6 congruence in right triangles are the triangles shown at the righ…
B. Yes, by the HL Theorem.
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quadrilateral fghj is dilated according to the rule ( d _ { o , \frac {…
\((-2,-4)\)
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are the two triangles congruent? if so, write the congruence statement.…
C. Yes, \(\triangle DEF\cong\triangle GHJ\) by the HL theorem.
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what is the value of x? 12 units 15 units 20 units 24 units
15 units
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triangle pqr was dilated according to the rule ( d_{o,2}(x,y)\to(2x,2y)…
\(\angle R\) corresponds to \(\angle P'QQ'\), Side \(RQ\) corresponds to side \(QQ'\)
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2.△abc and △pqr are right triangular sections of a fire escape, as show…
C. Yes, because the triangles are congruent by the Hypotenuse - Leg Theorem
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line segment jl is an altitude in triangle jkm. which statement explain…
JKM is not a right triangle because \(KL + LM eq15.3\)
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for what values of x and y are the triangles to the right congruent by …
\(x = 5\) and \(y = 2\)
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use the following diagram to complete the required information. m∠ros =…
$30^{\circ}28'10''$ (the second option)
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24° 59 60 is equivalent to degrees.
\(25\)
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which triangle is similar to \\( \\triangle jkl \\)? \\( \\bigcirc \\tr…
\(\triangle MKL\)
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use the given figure to complete the statement below. m\\angle cob and …
\(DOE\)
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triangle abc will be dilated according to the rule ( d_{f,0.25}(x,y) ),…
\((-2,-1)\)
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use the given figure to answer the question below. ray \\( \\overline {…
20°
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what ray is a common side of ∠eob and ∠boa?
Ray \(OB\)
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in the diagram, the length of (overline{yz}) is twice the length of (ov…
\(5\sqrt{3}\) units
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which of the following does not have a measure of 40 degrees? ∠aox ∠coa…
\(\angle DOA\)
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one leg of an isosceles right triangle measures 5 inches. rounded to th…
C. 7.1 inches
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triangle fgh is an isosceles right triangle with a hypotenuse that meas…
8 units
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what is the length of bc, rounded to the nearest tenth? 13.0 units 28.8…
31.2 units
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δqrs is a right triangle. select the correct similarity statement. δstr…
\(\triangle STR\sim\triangle SQR\) (the third option)
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line segment wx is the radius of circle x, and line segment zy is the r…
\(324\pi\) units\(^{2}\)
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the measures of ∠g and ∠h in △fgh are shown. what is the value of x? 20…
\(13\)
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the smallest of the three circles with center d has a radius of 8 inche…
\(464\pi\ in^{2}\)
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in \\( \\triangle k l m \\), the coordinates of the vertices are \\( k …
The length of \(\overline{LM}\) is \(2\sqrt{10}\approx6.32\).
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the distance between vega and deneb is 6 coordinates. the distance betw…
\(12.5\)
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the diagram shows one way to develop the formula for the area of a circ…
\(A=\frac{1}{2}(2\pi r)(r)\)
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what is the value of c? 4 units 5 units 6 units 7 units
5 units
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lines $l$, $m$, and $n$ are parallel and cut by transversal $p$. enter …
The value of \(x\) is \(26\) and the value of \(y\) is \(36\).
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cx is an altitude in triangle abc. which statements are true? select tw…
\(\triangle AXC\sim\triangle CXB\), \(\triangle ACB\sim\triangle AXC\)
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a circular garden with a radius of 8 feet is surrounded by a circular p…
\(178.98\ ft^{2}\) (corresponds to the second option \(178.98\ ft^{2}\))
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in a proof of the pythagorean theorem using similarity, what allows you…
the right triangle altitude theorem
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what is the length of side ts? 2√6 units 6√6 units 24 units 8 units
\(6\sqrt{6}\text{ units}\)
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triangle xyz is transformed to create triangle xyz. the side lengths of…
Yes, the pre - image and image have the same side length measures.
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fiona draws a circle with a diameter of 14 meters. what is the area of …
\(49\pi\space m^{2}\) (It seems there might be a typo in the options, as the correct area is \(49\pi\space m^{2}\))
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the sides of an equilateral triangle are 8 units long. what is the leng…
\(4\sqrt{3}\) units
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7. elenas bedroom is a rectangle with length 5 meters and width 3 meter…
a. Draw a rectangle with length \(10cm\) and width \(6cm\). b. The door should be \(1.6cm\) wide on the scale drawing. c. The actual measurements of the bed are \(2m\) by \(1.5m\).
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a transformation is shown in the diagram. which transformation is shown…
Quadrilateral \(DEFG\) is rotated to form quadrilateral \(D'E'FG'\).
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which transformation maps quadrilateral efgh to quadrilateral qrsp? dil…
rotation
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∠dac = ∠bad. what is the length of overline{bd}? round to one decimal p…
\(3.6\)
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what is the value of s? units
\(17\)
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the diagram shows a triangle. what is the value of u? u = °
\(2\)
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which transformations are nonrigid transformations? select two options.…
dilation, stretch
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triangle abc was translated to form abc. which describes the transforma…
It is rigid, It is isometric, The size is preserved.
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the diagram shows a triangle. what is the value of b? b =
\(85\)
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a transformation of \\( \\triangle stv \\) results in \\( \\triangle ut…
reflection
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what is the value of q? 4√5 2√14 20√5 64√5
\(2\sqrt{14}\)
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consider the two rectangles shown. what transformation maps rectangle q…
translation
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the diagram shows a triangle. what is the value of y? y = □°
\(33\)
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which statements are true regarding the area of circle d? select two op…
The area of the circle depends on the square of the radius; The area of circle D is \(324\pi\) \(cm^{2}\)
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what is the value of a? 6√2 9 8√3 36√2
\(6\sqrt{2}\)
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what is the value of x and the length of segment de? 1. \\( \\frac { 5 …
\(x = 6.6\); Length of \(\overline{DE}=16.2\) units
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the diagram shows a triangle. what is the value of x? x =
\(7\)