Agenda 1) Bell Work 2) Outcomes 3) Investigation with Rhombi 4) Special Parallelogram properties 5) Finding pieces of special parallelograms 6) Discuss Thursday/Friday quiz

Bell Work 3/12/13 1) Can you prove that the following is a parallelogram? If so, state why/why not. a) b) 2) Find the measure of the variables(b and c are parallelograms) a) b) c)

3/12/13 Outcomes I will be able to: 1) Determine if a parallelogram is a rectangle, rhombus or square 2) Find missing angles and side lengths of rectangles, rhombi and squares

Paper and Rhombi On the back of your bell work, draw two sets of parallel lines by tracing the top and the bottom of your straight edge. Your drawing should look like this: Label the vertices: A, B, C, D Measure AB, BC, CD, and AD What do you notice? A B D C

Rhombus The figure we just created was a Rhombus So, a Rhombus is a parallelogram with… All sides congruent Draw in the diagonals and label the point in the middle E. Look at the angles in the middle, what are they? 90° So the diagonals are perpendicular A B E D C

Rectangle Now draw a rectangle. ***Be sure to draw in the diagonals Measure the diagonals. What do you notice? They are congruent

Special Parallelogram Notes all sides congruent all angles congruent all sides are congruent and all angles are congruent ***So, a square is both a rhombus and a rectangle

Special Parallelogram Notes

Special Parallelogram Notes sometimes always sometimes sometimes always

Special Parallelogram Notes Example 3: EFGH is a rectangle. K is the midpoint of FH. If EG = 8x – 16, what are EK and GK? E F If K is the midpoint of FH, then we know that it is also the midpoint of EG. K H G How do we solve for EK and GK? EK = 4x – 8 GK = 4x - 8

Special Parallelogram Notes It has four congruent sides it has four congruent angles it has four congruent sides and four congruent angles(it is a rhombus and a rectangle)

Examples What do we know about the sides of a rhombus? They are equal: So: 2x = 3x - 16 x = 16

Examples What do we have to solve for first? What do we know about the angles of a square? They equal 90°. So: 8x + 10 = 90 x = 10 What do we know about the sides of a square? They are equal. So: 2y = x + 4. Substituting 10 in for x. 2y = 14 y = 7

Special Parallelogram Notes rhombus perpendicular

Special Parallelograms rhombus bisects

Special Parallelogram Notes rectangle diagonals Meaning: AC is congruent to BD.

Examples Rectangle Yes, because if the diagonals intersect at a 90° angle that means the shape is rhombus. If the shape is both a rhombus and a rectangle, then it is a square. Mr McGrew ur the man

Quiz Items Special Right Triangles Using Trig ratios to find missing side lengths in right triangles Using Trig ratios to find missing angles in right triangles Classifying polygons(Convex/Concave, and by name: pentagon, hexagon, etc.) Finding angle measures in quadrilaterals Properties of parallelograms