Vocab. Check How did you do? Some No All No Some All No Some All Some All

Unit Test Ch. 1-3 SOLUTIONS A C D C D B A D B A C A C B A or D

Review #6 1. ABC has vertices A(0,0), B(4,4) and C(8,0). What is the equation of the midsegment parallel to BC?

2. RED has vertices R(0,4), E(2,0), and D(6,4) 2. RED has vertices R(0,4), E(2,0), and D(6,4). Graph and write the equation for the perpendicular bisector of side RE. Then, find the circumcenter.

3. In ABC, centroid D is on median AM. AD = x + 6 DM = 2x – 12 Find AM.

Page 290 8-16E, 36-42 8)parallelogram 10) rectangle 12) isosceles trapezoid 14)kite 16)rectangle

36. next slide 37. T 38. F 39 F 40. T 41. F 42. F

Parallelogram A quadrilateral with both pairs of opposite sides parallel.

Rhombus A parallelogram with four congruent sides.

Rectangle A parallelogram with four right angles.

Square A parallelogram with four congruent sides and four right angles.

Kite A quadrilateral with 2 pairs of adjacent sides congruent and NO opposite sides congruent.

Trapezoid A quadrilateral with exactly one pair of parallel sides.

Isosceles Trapezoid A trapezoid whose nonparallel opposite sides are CONGRUENT.

Properties of Parallelograms Toolkit 6.2 Today’s Goal(s): To use relationships among sides and among angles of parallelograms. To use relationships involving diagonals of parallelograms or transversals.

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

5 Properties of a Parallelogram… Opposite sides are congruent. Opposite sides are also parallel. Opposite angles are congruent. The diagonals bisect each other. Consecutive angles are supplementary.

ANGLES… Opposite vs. Consecutive CONGRUENT SUPPLEMENTARY

EOC Review #6 Tuesday Plot the following points on a graph and decide if AD is an altitude, median, angle bisector or perpendicular bisector. A(6,7) B(8,2) C(2,2) D(6,2) Point C is a centroid. Solve for x.

Honors H.W. #28 pg. 297-300 #’s 2-34, 40-52 (evens)

Do you remember…? 5 Properties of a Parallelogram Hint: 2-sides, 2-angles, 1-diagonals

Proving a shape is a Parallelogram Toolkit 6.3 Today’s Goal(s): To use relationships among sides and among angles to determine whether a shape is a parallelogram.

There are 5 ways to PROVE that a shape is a parallelogram: Show that BOTH pairs of opposite SIDES are parallel. Show that BOTH pairs of opposite sides are congruent. Show that BOTH pairs of opposite ANGLES are congruent. Show that the DIAGONALS bisect each other. Show that ONE PAIR of OPPOSITE sides is both congruent & parallel.

6.3 Examples Determine whether the quadrilateral must be a parallelogram. Explain.

6.3 Examples #’s 10-15

#1 Find the value of x in each parallelogram. 1. 2. x = 60 a = 18

#2 Find the measures of the numbered angles for each parallelogram. 1. 2. 3. m1 = 38 m1 = 81 m1 = 95 m2 = 32 m2 = 28 m2 = 37 m3 = 110 m3 = 71 m3 = 37

#3 Find the value of x for which ABCD must be a parallelogram. 1. 2. x = 5 x = 5

#4 Use the given information to find the lengths of all four sides of  ABCD. The perimeter is 66 cm. AD is 5 cm less than three times AB. x = 9.5 BC = AD = 23.5 AB = CD = 9.5

#5 In a parallelogram one angle is 9 times the size of another #5 In a parallelogram one angle is 9 times the size of another. Find the measures of the angles. 18 and 162

EOC Review #6 Wednesday ABC has a perimeter of 10x. The midpoints of the triangle are joined together to form another triangle. What is the difference in the perimeters of the two triangles? Where is the center of the largest circle that you could draw INSIDE a given triangle?

Let’s set up some proofs! 

You try this one…

Ex.2: Two-Column Proof

Hmm… is there more than one way to write this proof? Statements Reasons

Special Parallelograms Toolkit #6.4 Today’s Goal(s): To use properties of diagonals of rhombuses and rectangles.

Rhombus A rhombus has ALL the properties of a parallelogram, PLUS… All four sides of a rhombus are congruent. Each diagonal of a rhombus BISECTS two angles. The diagonals of a rhombus are perpendicular.

Rectangle A rectangle has ALL the properties of a parallelogram, PLUS… All four angles of a rectangle are 90. The diagonals of a rectangle are congruent. AC  BD

Square A square has ALL the properties of a parallelogram, PLUS ALL the properties of a rhombus, PLUS ALL the properties of a rectangle.

So, that means that in a square… All four sides are congruent. All four angles are 90. The diagonals BISECT each other. The diagonals are perpendicular. The diagonals are congruent.

Ex.1: Find the measures of the numbered angles in each rhombus. a. b.

Ex.1: You Try… c.)

Ex.2: Find the length of the diagonals of rectangle ABCD. a.) AC = 2y + 4 and BD = 6y – 5 b.) AC = 5y – 9 and BD = y + 5

In-Class Practice #1-3

#4-6

#7-9