Vocab. Check How did you do? 1. Some 2. No 3. Some 4. All 5. No 6. Some 7. No 8. Some 9. All 10....

Vocab. CheckHow did you do?

1. Some

2. No

3. Some

4. All

5. No

6. Some

7. No

8. Some

9. All

10. Some

11. Some

12. No

13. No

14. Some

15. All

16. All

17. Some

18. No

19. Some

20. All

Unit Test Ch. 1-3SOLUTIONS

1. A

2. A

3. C

4. D

5. C

6. C

7. C

8. D

9. C

10. B

11. A

12. B

13. D

14. D

15. B

16. A

17. C

18. C

19. A

20. C

21. B

22. A or D

23. C

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). 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):1. To use relationships among sides and among

angles of parallelograms.2. 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…1. Opposite sides are congruent.2. Opposite sides are also parallel.3. Opposite angles are congruent.4. The diagonals bisect each other.5. Consecutive angles are

supplementary.

ANGLES…Opposite vs. Consecutive

CONGRUENT SUPPLEMENTARY

EOC Review #6Tuesday

1. 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)

2. Point C is a centroid.

Solve for x.

Honors H.W. #28pg. 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

ParallelogramToolkit 6.3

Today’s Goal(s):1. 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:

1. Show that BOTH pairs of opposite SIDES are parallel.2. Show that BOTH pairs of opposite sides are congruent.3. Show that BOTH pairs of opposite ANGLES are congruent.4. Show that the DIAGONALS bisect each other.5. Show that ONE PAIR of OPPOSITE sides is both congruent &

parallel.

6.3 ExamplesDetermine 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

#2Find the measures of the numbered angles for each parallelogram.

1. 2. 3.

m1 = 38 m1 = 81 m1 = 95m2 = 32 m2 = 28 m2 = 37m3 = 110 m3 = 71 m3 = 37

#3Find the value of x for which ABCD must be a parallelogram.

1. 2.

x = 5 x = 5

#4Use 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 = 23.5AB = CD = 9.5

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

18 and 162

EOC Review #6 Wednesday

11 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?

2. 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 ParallelogramsToolkit #6.4

Today’s Goal(s):1. To use properties of

diagonals of rhombuses and rectangles.

RhombusA rhombus has ALL the properties of a parallelogram, PLUS…

1. All four sides of a rhombus are congruent.2. Each diagonal of a rhombus BISECTS two angles.3. The diagonals of a rhombus are perpendicular.

RectangleA rectangle has ALL the properties of a parallelogram, PLUS…

1. All four angles of a rectangle are 90.2. The diagonals of a rectangle are

congruent.

AC BD

A square has ALL the properties of a parallelogram, PLUS

ALL the properties of a rhombus, PLUS

ALL the properties of a rectangle.

Square

So, that means that in a square…

1. All four sides are congruent.2. All four angles are 90.3. The diagonals BISECT each other.4. The diagonals are perpendicular.5. 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