21
Sometimes, Always or Never never always never sometime s sometime s 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.
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
