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Aim 6.6: To complete proofs using properties of Parallelograms

Aim 6.6: To complete proofs using properties of Parallelograms. A. B. Do Now: 1. Name how the two triangles are congruent in the rectangle below: 2. Find the measure of an exterior angle in a pentagon: Homework: Packet page 3 #5 & 6. C. D. Example #1:.

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Aim 6.6: To complete proofs using properties of Parallelograms

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  1. Aim 6.6: To complete proofs using properties of Parallelograms A B Do Now: 1. Name how the two triangles are congruent in the rectangle below: 2. Find the measure of an exterior angle in a pentagon: Homework: Packet page 3 #5 & 6 C D

  2. Example #1: Aim 6.6: To complete proofs using properties of Parallelograms & Trapezoids

  3. Example #2: • Given: Rectangle ABCD E is the midpoint of DC • Prove: Angle 1 Angle 2 E C D 1 2 Aim 6.6: To complete proofs using properties of Parallelograms & Trapezoids A B

  4. Answer: Statement Reason 1. Rectangle ABCD 1. Given 2. AD BC 2. 3. Angle ADE and Angle BCE 3. are congruent right angles 4. 4. 5. 5. 6. 6. SAS 7. Angle 1 Angle 2 7. Opposite sides of a rectangle are congruent A rectangle has 4 congruent right angles E is the midpoint of DC Given DE EC A midpoint cuts a line in ½ ADE BCD Aim 6.6: To complete proofs using properties of Parallelograms & Trapezoids CPCTC

  5. Example #3: Given: Isosceles Trapezoid ABCD Prove: ADB DBC B A D C Aim 6.6: To complete proofs using properties of Parallelograms & Trapezoids

  6. Answer: Statement Reason • Isosceles Trapezoid ABCD 1. Given • AD BC 2. The legs of a Isosceles Trapezoid are • AB is parallel to DC 3. A trapezoid has parallel bases • Angle ABD Angle BDC 4. When lines are parallel, alternate interior angles are • BD BD 5. Reflexive Property • ABD BDC 6. SAS Aim 6.6: To complete proofs using properties of Parallelograms & Trapezoids

  7. 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 G 1 2 D C F E Aim 6.6: To complete proofs using propertiesof Parallelograms & Trapezoids

  8. Example #3: August 2009 Regents Given: Quadrilateral ABCD, diagonal AFEC, AE FC, BF is perpendicular to AC, DE is perpendicular to AC, Angle 1 Angle 2 Prove: ABCD is a parallelogram B C E F Aim 6.6: To complete proofs using properties of Parallelograms A D

  9. Exit Ticket: • True or False: The bases of a parallelogram are congruent? • Name the missing step in the proof: Statement Reason • AB CD 1. Given • EF EF 2. Reflexive • 3. Addition Axiom Aim 6.6: To complete proofs using properties of Parallelograms & Trapezoids

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