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Aim 6.5: To prove two triangles in a Quadrilateral are congruent Do Now: (Show all work) 1. Determine the number of degrees on an interior angle in a polygon with 8 sides: 2. What is the measurement of an exterior angle of a 9 sided polygon? Homework: Packet Page 12 #2 & 3 Aim 6.5: To prove two triangles in a Quadrilateral are congruent Remember Proofs? • Five ways to say two triangles are congruent: 1. SSS 2. SAS 3. ASA 4. AAS 5. HL • Angles can be congruent because of perpendicular and parallel lines • Bisectors and medians create congruent sides • Always look to prove 2 triangles are congruent first. Then you can use CPCTC. Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example #1: Given: Triangles ABC & CDE C is the midpoint of BD AB is parallel to DE A Prove: AB DE D C B E Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example #2: Given: Parallelogram ABCD Prove: AEB A DEC B E D C Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example: #3 Given: Parallelogram PQRS PE SQ & RF SQ Prove: SE P QF Q F E S R Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example #3: Statement 1. Parallelogram PQRS 2. PS QR 3. PS || QR 4. Angle PSE Angle RQF 5. PE SQ & RF SQ 6. Angle PES & Angle RFQ are right angles 7. Angle PES Angle RFQ 8. PES RFQ 9. SE QF Reason 1. Given 2. Opposite sides of a p-gram are 3. Opposite sides of a p-gram are || 4. Alternate interior angles are 5. Given 6. Perpendicular lines form right angles 7. All right angles are 8. AAS 9. CPCTC Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example #4: Packet page 1 #1 Given: Rectangle ABCD DF CE Prove: a) ADE BCF b) Angle 1 Angle 2 c) GF GE A D B 1 F 2 E C Aim 6.5: To prove two triangles in a Quadrilateral are congruent Exit Ticket: • True or False: The opposite sides of a Parallelogram are congruent but not parallel • We can say AC AC by _____________ • Name the 5 methods we can use to prove two triangles are congruent: