Congruent Figures

Quadrilateral A B C D is rotated 145 degrees about point T to form quadrilateral A prime B prime C prime D prime. Quadrilateral ABCD is rotated 145° about point T. The result is quadrilateral A'B'C'D'. Which congruency statement is correct? ABCD ≅ A'B'C'D' ABCD ≅ A'D'C'B' CDAB ≅ A'D'C'B' CDAB ≅ C'B'A'D'

a

Triangle C D E is translated down and to the right to form triangle C prime D prime E prime. Triangle CDE is translated down and to the right, forming triangle C'D'E'. Which congruency statement is correct? ΔDCE ≅ ΔD'E'C' ΔDCE ≅ ΔD'C'E' ΔEDC ≅ ΔC'D'E' ΔEDC ≅ ΔC'E'D'

b

Triangle TRS is rotated about point X, resulting in triangle BAC. Triangle T R S is rotated about point X to form triangle B A C. The lengths of sides T R and A B are congruent, the lengths of sides A C and R S are congruent, and the lengths of sides T S and B C are congruent. If AB = 10 ft, AC = 14 ft, and BC = 20 ft, what is RS? 10 ft 14 ft 20 ft 24 ft

b

In the diagram, . Triangles P M N and Q S R are shown. The lengths of sides P N and R Q are congruent, the lengths of sides Q S and P M are congruent, and the lengths of sides M N and R S are congruent. If QR = 20 in., RS = 7 in., and SQ = 24 in., what is PN? 3 in. 7 in. 20 in. 24 in.

c

Rectangle ABCD is congruent to rectangle URST. Rectangles A B C D and U R S T are congruent. The length of sides A B is 9 millimeters and the length of sides R S is 15 millimeters. What is the area of rectangle URST? 24 mm 48 mm 135 mm² 144 mm²

c

Triangle G H J is rotated 90 degrees about point X to form triangle S T R. Triangle GHJ is rotated 90° about point X, resulting in triangle STR. Which congruency statement is true? TR ≅ GJ ∠S ≅ ∠H TS ≅ HG ∠R ≅ ∠G

c

Triangle X Y Z is translated up 2 and right 3 units to form triangle C A B. Triangle XYZ was translated up 2 and right 3 units, creating triangle CAB. Which relationship between the parts of the two triangles must be true? ∠X ≅ ∠A ZX ≅ CA YZ ≅ AB ∠Z ≅ ∠C

c

Triangles Q R P and X Y Z are congruent. Angle P Q R is 72 degrees. The lengths of sides A P and P R are 2.5 inches. Angle X Y Z is 36 degrees. The length of side X Y is 1.4 inches. What is the perimeter of ΔYXZ? 3.5 in. 5.3 in. 6.4 in. 7.8 in.

c

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? 6 cm 8 cm 9 cm 10 cm

d

The figure was created by repeatedly reflecting triangle NMP. A figure is created by continuously reflecting triangle N M P. The length of side N M is 6 inches, the length of side M P is 4 inches, and the length of side N P is 8 inches. What is the perimeter of the figure? 36 in. 42 in. 44 in. 48 in.

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