Sometimes, Always or Never

never

always

never

sometimes

sometimes

1. A trapezoid is a ll gram.

2. A rhombus is a ll gram.

3. A parallelogram is a

trapezoid.

4. A rhombus is a square.

5. The diagonals of a rhombus are congruent .

Given : D is the midpoint of AB E is the midpoint of BC

Find: x, y and z.

B

D E

A C

5x + 3

3x + 15

2y

50

6z - 8

4z + 12

x = 6, y = 25 and z =2

7

Given: EF = FG = GHFind x and y if AB = 2x+12,

BC = 4y and CD = 7x-8

A E

B F

C G

D H

x = 4, y = 5

Prove that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

s r

1) AC and DB given

bisect each other at E

2) E is the midpoint of def bisector

AC and DB

3) AECE, DEBE def midpoint

4) 1 2 vertical ’s thm.

5) AED CEB SAS post.

6) AD CB, 3 4 CPCTC

7) AD // CB alt. int ’s lines ll

8) ABCD is a //gram one pair opp sides // & thm.

A B

E

D C

1 23

4

If CD is a median and m 1 = 20 find the measures of the rest of the numbered angles.

A

1

D

C 2 3 B

4

5

m 2 = 70

m 3 = 70

m 4 = 140

m 5 = 20

A B

C D

E F

Find x if CD = 5x + 2,

AB = x + 3 and EF = 4x + 10

5

9x

A

1

D

C 2 3 B

4

5

Find the measure of the numbered angles if m 1 = 60.

m 2 = 30

m 3 = 30

m 4 = 60

m 5 = 60

A B

C D

E F

Find x if CD = 15,

AB = 12 and EF = x

18x

A

B C

D F E

Given B, C and F are midpoints of DA, AE and DE respectively. Find BC, CF and BF, if AE = 22, DE = 25 and AD = 27.

12.5

13.5 11

Prove that if one pair of opposite sides of a quadrilateral are both congruent and parallel then the quadrilateral is a parallelogram.

A B

D C s r

1) AD//BC, ADBC given

2) Draw DB through any two pts. Exactly 1 line

3) ADB CBD alt. int ‘ s thm.

4) DB DB reflexive prop ‘ s

5) ABD DCB SAS post.

6) AB DC CPCTC

7) ABCD is a //gram both pair opp sides thm.

The segment that joins the midpoints of two sides of a triangle

1. is parallel to the third side;

2. is half as long as the third side.

6x 10

20 10

4y 10

Find x and y

x = , y = 53

10

If three parallel lines cut off congruent segments on one transversal, then they cut off

_________ _________on every transversal.

congruent segments

Find x

4x + 5 8x - 35

x = 10

If two lines are parallel, then all points on one

line are _______ from the other line.

equidistant

What are the 5 ways to prove a quadrilateral is a parallelogram?

Show that both pairs of opposite sides are parallel.

Show that both pair of opposite sides are congruent.

Show that one pair of opposite sides are both // and .

Show that both pair of opposite angles are congruent.

Show that the diagonals bisect each other.

Sometimes, Always or Never

always

sometimes

always

never

1.Adjacent sides of a rhombus are congruent.

2. Adjacent sides of a trap are congruent.

3. Both pair of opposite angles of a rectangle are congruent.

4. A square is a trapezoid.

Name the quadrilateral by its best name:

SNOW S(0, 3)N(5, 4)O(6, -1)W(1, -2)

square