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Three figures exist such that ABCD ≅ GHIJ and BCDA ≅ RSTU.If GH = 6 cm, HI = 8 cm, IJ = 10 cm, and GJ = 9 cm, what is TS? : XX8 cm
Triangle ABC is congruent to triangle XYZ. In ΔABC, AB = 12 cm and AC = 14 cm. In △XYZ, YZ = 10 cm and XZ = 14 cm.What is the perimeter of ΔABC? : 36cm
Which of these triangle pairs can be mapped to each other using a single translation? : D
Two rigid transformations are used to map ΔHJK to ΔLMN. The first is a translation of vertex H to vertex L. What is the second transformation? : a rotation about point H
Which of these triangle pairs can be mapped to each other using a single reflection? : A
If bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Check all that apply. : m∠ABC = 125° and AB ≅ DBCD = 52 cmAB = 29 cm
How can ΔWXY be mapped to ΔMNQ?First, translate vertex W to vertex M.Next, reflect ΔWXY across the line containing____ : line segment WX
Triangles RQS and NTV have the following characteristics:• Right angles at ∠Q and ∠T • RQ ≅ NTCan it be concluded that ΔRQS ≅ ΔNTV by SAS? Why or why not? : No, it is necessary to know that another set of corresponding sides is congruent.
Which of these triangle pairs can be mapped to each other using two reflections? : XXd
Can a translation and a reflection map QRS to TUV? Explain why or why not. : Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.
The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map ABC onto FED? : reflection, then translation
Triangle ABC is congruent to A'BC' by the HL theorem.What single rigid transformation maps ABC onto A'BC'? : reflection
The triangles are congruent by SSS.Which transformation(s) can be used to map one triangle onto the other? : reflection onlyrotation, then translation
Which explains whether ΔFGH is congruent to ΔFJH? : They are not congruent because only one pair of corresponding sides is congruent.
Which angle has a measure equal to the sum of the m∠SQR and the m∠QRS? : XX∠SRE
What is the value of x? : x=40
Which statement regarding the interior and exterior angles of a triangle is true? : An exterior angle is supplementary to the adjacent interior angle.
What is the value of x? (35, 58) : x = 93
Which statements about the diagram are true? Check all that apply. (DFE 4,9) : a, c, e
The value of x must be greater than (12, 15) : 3
Triangle QRS has the angle measures shown.m∠Q = (1x)°m∠R = (3x)°m∠S = (6x)°The measure of the obtuse angle equals : 108
to make a triangle: https://www.geogebra.org/m/JHgTXKrt : ...
In the triangles, QR = DE and SR = FE.Which statement about the sides is true? : DF < QS
Gene starts from home and travels 3 miles north to the shopping mall. From the shopping mall, he travels 2 miles west to the library. Then, from the library, he travels about 3.6 miles to return home. The entire trip forms a triangle.The largest angle made during his trip is at : the mall
In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet. What is RS? : 7 feet
In triangle DEF, CG = (x + 5) units and DG = (3x - 2).What is DG? : 34
Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x - 1) units.What is AF? : 51 units
In triangle NLM, point S is the centroid, QS = (3x - 5) cm, and NS = (4x) cm.What is NS? : 20 cm
The figure shows a circle inscribed in a triangle.To construct the inscribed circle, angle bisectors were first constructed at each angle of the triangle. Which happened next? : XXA circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.
Point Y is the circumcenter of ΔDEF.Find the length of FY.FY measures ____ units : 22
Point X is the circumcenter of ΔABC.What is the length of MB? : 2.5 cm
Point P is the incenter of ΔRST.Which must be true? : BP=PC
In triangle ABC, BG = 24 mm. What is the length of segment GE? : 12
Consider the triangle.The measures of the angles of the triangle are 32°, 53°, 95°. Based on the side lengths, what are the measures of each angle? : b: mA = 32°, mB = 53°, mC = 95°
ZE is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and .Which must be true? : Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle? : 72
Which diagram shows possible angle measures of a triangle? : B
Janelle says that lines l and m are skew lines.Is Janelle correct? : No, because the lines are in the same plane.
Consider the diagram.Which line segment has the same measure as TQ? : TR
In the diagram, line a is the perpendicular bisector of KM.What is the length of KM? : 80 units
The m6 = (11x + 8)° and m7 = (12x - 4)°What is the measure of 4? : m4 = 40°
Two parallel lines are crossed by a transversal.What is the value of x? : x = 37(3x+4 \ 115)
Two parallel lines are crossed by a transversal.If m6 = 123.5°, then m1 is : 56.5
Given: m || n and p is a transversalProve: m2 = m7What is the missing reason in the proof?6? : transitive property
Two parallel lines are crossed by a transversal.What is the value of x? : x = 115( x \ 115)
Two parallel lines are crossed by a transversal.What is the value of h? : h = 60(120 \ h)
Parallel lines e and f are cut by transversal b.What is the value of y? : 130
What must be the value of x so that lines a and b are parallel lines cut by transversal f?The value of x is : 22
A line has a slope of . Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply. : (-3, 4) and (2, 0)(1, -1) and (6, -5)
Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)? : line HJ
Which point is on the line that passes through point H and is perpendicular to line FG? : (-6, 10)
Lines MN and PQ are parallel. Lines RS and TV intersect them.Which statements are true about these lines? Check all that apply. : The slope of line MN is .The slope of line RS is .Line RS is perpendicular to both line MN and line PQ.
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)? : D:y - 1=3/2 (x + 3)
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply. : XX2x + 5y = −10y + 4 = -(x - 5)for sure B
The given line segment has a midpoint at (−1, −2).What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment? : y = −4x − 6
What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )? : y = −6
What is the equation of the line that is parallel to the given line and has an x-intercept of -3? : XXc:y = -3/2x + 3
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? : x + 2y = 8
What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)? : D:y = 3x − 5
What must be the value of x so that lines c and d are parallel lines cut by transversal p? : 18
Which point is on the line that passes through point R and is perpendicular to line PQ? : (-4, -8)
Which statement best explains the relationship between lines AB and CD? : They are parallel because their slopes are equal
Triangle 1 undergoes four different transformations. The results of these transformations are shown.Which statement best describes one of these transformations? : Triangle 1 is rotated to result in triangle 2.
Triangle ABC was translated to form A'B'C'.Which describes the transformation? Check all that apply. : It is rigid.It is isometric.The size is preserved
Which transformation maps the pre-image, DEFG, to the image, D'E'F'G'? : The transformation is a reflection.
ΔA'B'C' was constructed using ΔABC and line segment EH.For the transformation to be a reflection, which statements must be true? Check all that apply. : BD = DB'CG = GC'm∠EFA = 90°The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
What is the rule for the reflection? : rx-axis(x, y) → (x, -y)
Figure ABCD was reflected across the x-axis to create figure A'B'C'D'.What are the coordinates of the pre-image of B'? : (-8, -2)
A triangle on a coordinate plane is translated according to the rule T-8, 4(x, y). Which is another way to write this rule? : (x, y) → (x - 8, y + 4)
Irina wants to tile her floor using the translation shown below. Which is the rule for this translation? : XXT-2, 3(x, y)
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation? : (x, y) → (x - 3, y + 5)
Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y - 3.5) to create the image ΔA'B'C' shown on the coordinate plane.Which graph shows the pre-image, ΔABC? : XXba
Square ABCD was translated using the rule (x, y) → (x - 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D' in the image are (9, -8)? : (13, -23)
If a translation of (x, y) → (x + 6, y - 10) is applied to figure ABCD, what are the coordinates of D'? : (1, -12)
Triangle RST was transformed using the rule (x, y) → (-x, -y). The vertices of the triangles are R (1, 1)S (3, 1)T (1, 6) R' (-1, -1)S' (-3, -1)T' (-1, -6)Which best describes the transformation? : The transformation was a 180° rotation about the origin.
Which shows the image of quadrilateral ABCD after the transformation R0, 90°? : XXd
Triangle ABC was transformed using the rule (x, y) → (-y, x). The vertices of the triangles are shown.A (-1, 1)B (1, 1)C (1, 4) A' (-1, -1)B' (-1, 1)C' (-4, 1)Which best describes the transformation? : The transformation was a 90° rotation about the origin.
Parallelogram ABCD is rotated to create image A'B'C'D'.Which rule describes the transformation? : (x, y) → (y, -x)
A triangle has vertices at L(2, 2), M(4, 4), and N(1, 6). The traingle is transformed according to the rule R0, 180°.Which statements are true regarding the transformation? Check all that apply. : The rule for the transformation is (x, y) → (-x, -y).The coordinates of L' are (-2,-2).The coordinates of N' are (-1,-6)
Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(-1, 2). The image of triangle XYZ after a rotation has verticesX'(-3, 1), Y'(0, 0), and Z'(-2, -1). Which rule describes the transformation? : R0, 90°
Which rule describes the composition of transformations that maps ΔABC to ΔA"B'C"? : RB', 270° • rm
What is the final transformation in the composition of transformations that maps pre-image GHJK to image G'H"J"K"? : a reflection across line m
If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have? : 20
What is the order of rotational symmetry for a rhombus? : 2
Which figure has the same order of rotational symmetry as a rectangle? : rhombus
What is the smallest angle of rotational symmetry for a square? : 90
How can a regular hexagon be folded to show that it has reflectional symmetry? : XXFold the hexagon along a line from a vertex to the midpoint of an opposite side.Fold the hexagon along a line connecting the two midpoints of adjacent sides.
Which letter in the word HAPPY has an order 2 rotational symmetry? : H
A composition of transformations maps ΔKLM to ΔK"L"M".The first transformation for this composition is_________ , and the second transformation is a translation down and to the right. : a 270 rotation around p
Complete the statement about the transformation.Point F' corresponds to : point F
Triangle QRS is transformed as shown on the graph.Which rule describes the transformation? : R0, 270°
Quinton tried to transform triangle FGH according to the rule (x, y) → (-y, x). Which best describes his attempt? : Correct. He transformed the triangle according to the rule (x, y) → (-y, x).
Cedric applied the rule rm • RP, 90°(x, y) to figure WXYZ.What mistakes did he make? Check all that apply. : He applied the reflection to the pre-image first.He used an incorrect angle of rotation around point P.
