Aim 6.5: To prove two triangles in a Quadrilateral are congruent

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Presentation transcript:

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

Remember Proofs? Five ways to say two triangles are congruent: 1. SSS 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 Prove: AB DE D A C B E

Example #2: Given: Parallelogram ABCD Prove: AEB DEC A B E D C Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example #2: Given: Parallelogram ABCD Prove: AEB DEC A B E D C

Example: #3 Given: Parallelogram PQRS PE SQ & RF SQ Prove: SE QF P Q F Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example: #3 Given: Parallelogram PQRS PE SQ & RF SQ Prove: SE QF P Q F E S R

Aim 6.5: To prove two triangles in a Quadrilateral are congruent Example #3: Statement Reason Parallelogram PQRS 1. Given PS QR 2. Opposite sides of a p-gram are PS || QR 3. Opposite sides of a p-gram are || Angle PSE Angle RQF 4. Alternate interior angles are PE SQ & RF SQ 5. Given Angle PES & Angle RFQ 6. Perpendicular lines are right angles form right angles Angle PES Angle RFQ 7. All right angles are PES RFQ 8. AAS SE QF 9. CPCTC

Example #4: Packet page 1 #1 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 B 1 2 D C F E

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: