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5.1 Congruence and Triangles Unit 5 corresponding sides and angles Classification of Triangles Oct 108:04 AM Sides: Angles: Oct 108:04 AM Figures are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent! C P N M E Oct 108:04 AM D Oct 108:04 AM P X K W U 130 H Y J Q R S Oct 108:04 AM T 8 Oct 108:04 AM 1 A B Oct 108:04 AM 35 35 C D Oct 108:04 AM TicketouttheDoor Oct 108:04 AM Oct 108:04 AM 5.2 Proving Triangles are Congruent: SSS and SAS Assignment: pages 236237 #1426, 34, 38, 40, 41, 42, 44 Oct 108:04 AM SideSideSide Congruence Postulate (SSS) If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Oct 108:04 AM 2 SideAngleSide Congruence Postulate (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. What is an included angle? W Z Y X Oct 108:04 AM c. H J K Oct 108:04 AM M N Oct 108:04 AM Let's try a proof! Oct 108:04 AM L Oct 108:04 AM Maybe just one more... Oct 108:04 AM 3 TicketouttheDoor Assignment: pages 245246 #1026 even, 30, 34 Oct 108:04 AM Oct 108:04 AM 5.3 Proving Triangles are Congruent: ASA and AAS AngleSideAngle Congruence Postulate (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. c. Oct 108:04 AM d. Oct 108:04 AM AngleAngleSide Congruence Theorem (AAS) If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. What additional congruence is needed to show that triangle QPS triangle QRS by the AAS Congruence Theorem? Oct 108:04 AM Oct 108:04 AM 4 White Board Practice!!! Oct 108:04 AM Mar 157:07 AM Mar 157:11 AM Mar 157:15 AM 5.4 HypotenuseLeg Congruence Theorem (HL) If the hypotenuse and a leg of a RIGHT triangle are congruent to the hypotenuse and a leg of a second RIGHT triangle, then the two triangles are congruent. Assignment: pages 254-255 #10-32 even Oct 108:04 AM Oct 108:04 AM 5 Summary SSS SAS Is it possible to show that triangle ABC is congruent to triangle ADC using the HL Congruence Theorem? Explain your reasoning. ASA A AAS D B HL C Oct 108:04 AM Oct 108:04 AM You try: D A c. C B Oct 108:04 AM E Oct 108:04 AM Ticket out the Door Assignment: pages 260262 #10, 12, 16, 18, 20, 22, 26, 30 Oct 108:04 AM Oct 108:04 AM 6 5.6 Angle Bisectors and Perpendicular Bisectors How do you find distance from a point to a line? 5.15.4 review: page 683 #115 Equidistant when a point is the same distance from one line as it is from another line. Oct 108:04 AM Oct 108:04 AM Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Oct 108:04 AM Oct 108:04 AM Use the diagram to find AB. G Use the diagram to find GH. 3x+2 J H 5x12 K Oct 108:04 AM Oct 108:04 AM 7 Assignment: page 277 #1012, 1419 Oct 108:04 AM Oct 108:04 AM 5.7 Reflections Reflection a transformation that creates a mirror image Properties of reflections: 1) The reflected image is congruent to the original figure. 2) The orientation of the reflected image is reversed. 3) The line of reflection is the perpendicular bisector of the segments joining the corresponding points. Oct 108:04 AM Oct 108:04 AM Oct 108:04 AM Oct 108:04 AM 8 5.7 continued Symmetry Assignments: pages 286287 #816, 18, 31, 34, 36 worksheet coloring page Oct 108:04 AM Symmetry of Shapes Activity Oct 108:04 AM Line of symmetry a line of reflection How many lines of symmetry are in a square? Oct 108:04 AM Oct 108:04 AM What is a kaleidoscope? Oct 108:04 AM Oct 108:04 AM 9 Assignments: Test Review: pages 287288 #2129, 34, 36, 37, 39 ONE partner worksheet complete pages 683684 #129 all finish reflection coloring page Oct 108:04 AM Oct 108:04 AM Oct 228:15 AM Oct 154:13 PM 10