Quadrilateral Family Worksheets - Definitions, Properties Chart, Family Tree And Venn Diagram Page 13
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13Definition of Rectangle: It is a rectangle it is a parallelogram with four right angles.
Definition of Rhombus: It is a rhombus it is a parallelogram with four congruent sides.
Definition of Trapezoid: It is a trapezoid it is a quadrilateral with exactly one pair of parallel sides.
Def of Isosc Trapezoid: It is an isosceles trapezoid it is a trapezoid whose nonparallel sides are congruent.
Definition of Kite:
It is a kite it is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.
You may use any theorems (but write them out!) and definitions above to prove the following.
You may also use this unnamed shortcut (write it out!): Congruent supplementary angles are right.
6. Prove Theorem 6-9 (rhombus each diagonal bisects two angles of
10. Prove Theorem 6-16 (isosceles trapezoid diagonals are
the rhombus).
congruent), using Theorem 6-15 (but write it out).
ABCD
Given:
is a rhombus.
Given:
ABCD
is an isosceles trapezoid with
.
AB CD
Prove:
and
.
1
2
5
6
3
4
7
8
C
B
Prove:
AC
BD
A
B
2
3
E
1
4
A
D
C
D
7. Prove Theorem 6-10 (rhombus diagonals are perpendicular).
11. Prove Theorem 6-17 (kite diagonals are perpendicular).
Given:
ABCD
is a rhombus.
ABCD
Given:
is a kite with
,
, and
and
AB
AD
BC
DC
AC
Prove:
AC
BD
E
intersect at point
.
BD
A
B
Prove:
B
AC
BD
E
17
10
C
A
E
C
D
8. Prove Thm 6-11 (rectangle diagonals are ).
Given:
ABCD
is a rectangle.
D
Prove:
AC
BD
A
B
12. Prove this shortcut statement: If angles are congruent and
supplementary, then they are right.
Given:
, and 1 and 2 are supplementary.
1
2
Prove: 1 and 2 are right angles.
D
C
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