L2.12 - Proofs about Quadrilaterals
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Comprehend a conjecture and express it (in writing) as a specific statement to prove.[/*][*]Critique others' reasoning (in spoken and written language) about quadrilaterals.[/*][*]Prove (in writing) theorems about quadrilaterals.[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Critique a proof about quadrilaterals.[/*][*]Prove theorems about quadrilaterals.[/*][*]Rewrite a conjecture so it is specific enough to prove.[/*][/list]
12.1: Play with Parallelograms
[color=#ff00ff]Open BOOK - Geo.2.12 Proofs about Quadrilaterals. Use the applet to explore the 4 quadrilaterals.[/color]
1. Which figures (if any) are always rectangles? Which figures can be dragged to make a rectangle?
2. Which figures (if any) are always parallelograms? Which figures can be dragged to make a parallelogram?
Six Properties of Parallelograms
[list=1][*][color=#9900ff]Opposite sides are congruent (AB [math]\cong[/math] CD).[/color][/*][*][color=#9900ff]Opposite angles are congruent ([math]\angle[/math]D [math]\cong[/math] [math]\angle[/math]B).[/color][/*][*][color=#9900ff]Consecutive angles are supplementary (m[math]\angle[/math]A + m[math]\angle[/math]D = 180°).[/color][/*][*][color=#9900ff]If one angle is right, then all angles are right.[/color][/*][*][color=#9900ff]The diagonals of a parallelogram bisect each other.[/color][/*][*][color=#9900ff]Each diagonal of a parallelogram separates it into two congruent triangles.[/color][/*][/list]
Show Properties 1 (Opposite sides are congruent) & 2 (Opposite angles are congruent) of Parallelograms.
Write an explanation in detail for property 1 of parallelograms.
1. Opposite sides are congruent.
Write an explanation in detail for property 2 of parallelograms.
2. Opposite angles are congruent.
Show Property 3 of Parallelograms (Consecutive angles are supplementary).
Write an explanation in detail for property 3 of parallelograms.
3. Consecutive angles are supplementary.
Show Property 4 of Parallelograms (If one angle is right, then all angles are right).
Write an explanation in detail for property 4 of parallelograms.
4. If one angle is right, then all angles are right.
Show Property 5 of Parallelograms (The diagonals of a parallelogram bisect each other).
Write an explanation in detail for property 5 of parallelograms.
5. The diagonals of a parallelogram bisect each other.[br]
Show Property 6 of Parallelograms (Each diagonal of a parallelogram separates it into two congruent triangles).
Write an explanation in detail for property 6 of parallelograms.
6. Each diagonal of a parallelogram separates it into two congruent triangles.
Review Rigid Transformations
Write a sequence of rigid motions to take figure ABC to figure DEF.
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Comprehend a conjecture and express it (in writing) as a specific statement to prove.[/*][*]Critique others' reasoning (in spoken and written language) about quadrilaterals.[/*][*]Prove (in writing) theorems about quadrilaterals.[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Critique a proof about quadrilaterals.[/*][*]Prove theorems about quadrilaterals.[/*][*]Rewrite a conjecture so it is specific enough to prove.[/*][/list]
Cool-Down: A Proof In Time Saves Nine
Elena wants to prove that a quadrilateral with 4 right angles must have congruent opposite sides. Explain to Elena how she can use the fact that all rectangles are parallelograms in her proof.
GLOSSARY
