2. Triangle ABC and triangle DEF are graphed on the set of axes below. 3. Quadrilateral ABCD is graphed on the set of axes below.

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1 Review Session 1 Pratie Problems l. The verties of AJKL have oordinates J(5,1), K( 2, 3), and Under whih transformation is the image AJ'K t L t not ongruent to AJKL? l) a translation of two units to the right and two units down 2) a ounterlokwise rotation of 180 degrees around the origin 3 a refletion over the x-axis 4) dilation with a sale fator of 2 and 9 entered at the origin 2. Triangle ABC and triangle DEF are graphed on the set of axes below. Whih sequene of transformations maps triangle ABC onto triangle DEF? 1) refletion over the x-axis followed by a refletion over the y-axis 2) a 1800 rotation about the origin followed by a refletion over the line y x 3) a 900 lokwise rotation about the origin followed by a refletion over the y-axis 4) a translation 8 units to the right and I unit up followed by a 900 ounterlokwise rotation about the origin 3. Quadrilateral ABCD is graphed on the set of axes below. When ABCD is rotated 900 in a ounterlokwise diretion about the origin, its image is quadrilateral A 'BCD'. Is distane preserved under this rotation, and whih oordinates are orret for the given vertex? no and C' (l, 2) no and D (2,4) yes and A ' (6, 2) 02 and B' ( 3, 4) 1 C 4. If AA'BC is the image of AABC, under whih transformation will the triangles not ongruent? 1) refletion over the x-axis 2 translation to the left 5 and down 4 ilation entered at the origin with sale tor 2 4) rotation of 2700 ounterlokwise about the origin

2 5. A sequene of transformations maps retangle ABCD onto retangle A"B"C"D", as shown in the diagram below. Whih sequene of transformations maps ABCD onto A 'B'C'D' and then s A 'BCD' onto A I a refletion followed by a rotation 2) a refletion followed by a translation 3) a translation followed by a rotation 4) a translation followed by a refletion 6. In the diagram of parallelogram FRED shown below, ED is extended to A, and AF is drawn suh that If mzr- 1240, what is mzafd9 1) ) ) 680 i 56 4) In the diagram below, whih single transformation was used to map triangle A onto triangle B? l) line refletion 3) dilation 4) translation 8. Whih statement is suffiient evidene that ADEF is ongruent to AABC? DE and BC-EF ZC=ZF 3) There is a sequene of rigid motions that maps AB onto DE, BC onto BF, and AC onto DF 4 There is a sequene of rigid motions that maps point A onto point D, B onto DE, and zb ontoze,? C

3 . Triangle ABC is graphed on the set of axes below. Graph and label AA 'B' C', the image of AABC after a refletion over the line x = 1. x 10. As graphed on the set of axes below, AA t B' C' is the image of AABC after a sequene of transformations. x 11. In parallelogranhbcd shown below, diagonals AC and BD interset at E. Prove: ZACD. ZCAB Statements Reasons l. tn parallelogram ABCD shown below, diagonals 1. Given 3' ah(s)

4 Guided Pratie Riqht Trianqles: 12. To find the sides of a right triangle use the Pythagorean Theorem. 2 2 (Remember that the a and b make up right angle) x 11 2 simpl$ð ) Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. d + ISO In the diagram below of AIIQP, side is extended through P to T, rnlqpt = 6.r + 20, mt.-hqp = x + 40, and mzphq = 4x 5. Find mlqpt. IS (6x + 20) 0 p (Not drawn to sale) ) Isoseles Triangles: The base angles of an isoseles triangle are equal in measure. The sides opposite the base angles in an isoseles triangle (alled legs) are equal in length. Given the following find the degrees in eah angle ofthe triangle. 50 OCA = 60 X SO

5 15) Centroid: 2:1 Ratio For seqments In triangle ABC, AD, CF, and BE are medians. If CF = 33, find CG and FG. 76) Side-Anqle Relationship The longest side is aross From the largest angle The medium length side is aross From the medium-sized angle The shortest side is aross From the smallest a 9 e In triangle DOG, 111<1) = 40, m<0 60, and m<g = 80. State the longest side of the triangle State the shortest side of the triangle 17. In the aompanying diagram,hk bisets IL and ZHE LK. Prove: HI KL Statements 1. HK bisets IL and Reasons 1. Given 2, 5 z I-JF- h Vs s, pçc

6 18) Given:Äb Il L Prove: AACB S G. 19) Graph and state the oordinates of AA'B'C', the image of AABC with A(1,2), B(3,O) and C(6,8)after the omposition T2,oo R1800.

7 20. Graph triangle ABC. A(l, 1), B(4, 5), C(3, 2) and reflet it through point (-2, 1). Label your image. Bi(-m-3) C' 010) Use rigid motions to explain why the pre-image and image are ongruent. pÿtsrjvr 21. In the diagram of trapezoid ABCD below, diagonals ACand BDinterset at E and A ABC ADCB. Whih statement is true based on the given information? 1) ACE BC 3) ZCDE= CAD 2) CD-AD 4) ZCDB= ZBAC pt D C