3. (9x + 9) x 45 5x. 5. (7x + 6)

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1 5 hapter eview 5.1 ngles of riangles (pp ) ynamic Solutions available at igideasath.com lassify the triangle by its sides and by measuring its angles. he triangle does not have any congruent sides, so it is scalene. he measure of is 117, so the triangle is obtuse. he triangle is an obtuse scalene triangle. 1. lassify the triangle at the right by its sides and by measuring its angles. Find the measure of the exterior angle (9x + 9) 46 x 45 5x Find the measure of each acute angle (7x + 6) 8x 7x (6x 7) 5.2 ongruent olygons (pp ) rite a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. he diagram indicates that F. orresponding angles F,, orresponding sides F,, F F 6. In the diagram, G. Identify all pairs of congruent corresponding parts. hen write another congruence statement for the quadrilaterals. G 7. Find m. U 74 S 290 hapter 5 ongruent riangles

2 5.3 roving riangle ongruence by SS (pp ) rite a proof. Given, rove SS SOS 2. Given ertical ngles ongruence heorem (heorem 2.6) SS ongruence heorem (heorem 5.5) ecide whether enough information is given to prove that using the SS ongruence heorem (heorem 5.5). If so, write a proof. If not, explain why quilateral and Isosceles riangles (pp ) In,. ame two congruent angles., so by the ase ngles heorem (heorem 5.6),. opy and complete the statement. 10. If, then. 11. If, then. 12. If S, then. 13. If S S, then. S 14. Find the values of x and y in the diagram. 26 8x 5y + 1 hapter 5 hapter eview 291

3 5.5 roving riangle ongruence by SSS (pp ) rite a proof. Given, rove SS SOS 2. Given eflexive roperty of ongruence (heorem 2.1) SSS ongruence heorem (heorem 5.8) 15. ecide whether enough information is given to prove that using the SSS ongruence heorem (hm. 5.8). If so, write a proof. If not, explain why. 16. ecide whether enough information is given to prove that using the ongruence heorem (hm. 5.9). If so, write a proof. If not, explain why. 5.6 roving riangle ongruence by S and S (pp ) rite a proof. Given, rove SS 1. SOS Given ertical ngles ongruence heorem (hm. 2.6) S ongruence heorem (hm. 5.11) 292 hapter 5 ongruent riangles

4 ecide whether enough information is given to prove that the triangles are congruent using the S ongruence heorem (hm. 5.11). If so, write a proof. If not, explain why. 17. FG, 18. U, S F G U S ecide whether enough information is given to prove that the triangles are congruent using the S ongruence heorem (hm. 5.10). If so, write a proof. If not, explain why. 19., 20., 5.7 Using ongruent riangles (pp ) xplain how you can prove that. If you can show that, then you will know that. ou are given and. ou know that by the eflexive roperty of ongruence (hm. 2.1). wo pairs of sides and their included angles are congruent, so by the SS ongruence heorem (hm. 5.5),. ecause corresponding parts of congruent triangles are congruent,. 21. xplain how to prove that. 22. rite a plan to prove that S U hapter 5 hapter eview 293

5 5.8 oordinate roofs (pp ) rite a coordinate proof. Given oordinates of vertices of O and y rove O (2j, 2j) (j, j) Segments O and have the same length. O = ( j 0) 2 + ( j 0) 2 = j 2 + j 2 = 2j 2 = j 2 = ( j 2j) 2 + ( j 0) 2 = ( j) 2 + j 2 = 2j 2 = j 2 Segments and have the same length. = = j 2 = (2j j) 2 + (2j j) 2 = j 2 + j 2 = 2j 2 = j 2 Segments O and have the same length. O = 2j 0 = 2j = 2j 0 = 2j O(0, 0) (2j, 0) x So, you can apply the SSS ongruence heorem (heorem 5.8) to conclude that O. 23. rite a coordinate proof. Given oordinates of vertices of quadrilateral O rove O O y (h, k + j) (0, j) (h, k) O(0, 0) x 24. lace an isosceles triangle in a coordinate plane in a way that is convenient for finding side lengths. ssign coordinates to each vertex. 25. rectangle has vertices (0, 0), (2k, 0), and (0, k). Find the fourth vertex. 294 hapter 5 ongruent riangles