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Algebra & Analytic Geometry
Unit 4 – Diagonals of Quadrilaterals
Name & Date
1) Consider the diagram below to complete the following.
C
B
A) Find each of the following lengths to the nearest
tenth of a centimeter.
E
D
AE =
CE =
AC =
BE =
DE =
BD =
B) Does BD bisect AC ? Explain.
C) Does AC bisect BD ? Explain.
A
D) Connect points A, B, C, and D to construct quadrilateral ABCD.
E) Use your protractor to determine if AC  BD ? Explain. Based on your findings fill in as many angles
as possible.
F) Are there any congruent triangles formed by the diagonals of ABCD? Explain why or why not using
congruence postulates or theorems. Be specific.
G) Classify ABCD and summarize your findings about the diagonals.
2) Consider the diagram below to complete the following.
C
A) Find each of the following lengths to the nearest
tenth of a centimeter.
B
E
D
AE =
CE =
AC =
BE =
DE =
BD =
B) Does BD bisect AC ? Explain.
C) Does AC bisect BD ? Explain.
A
D) Connect points A, B, C, and D to construct quadrilateral ABCD.
E) Use your protractor to determine if AC  BD ? Are there any congruent triangles formed by the
diagonals of ABCD? Explain why or why not using congruence postulates or theorems. Be specific.
F) Find m ABE . Based on your findings fill in as many angles as possible.
G) Classify ABCD and summarize your findings about the diagonals.
Algebra & Analytic Geometry
Unit 4 – Diagonals of Quadrilaterals
Name & Date
3) Consider the diagram below to complete the following.
B
C
E
A
D
A) Find each of the following lengths to the nearest tenth of a centimeter.
AE =
CE =
AC =
BE =
DE =
BD =
B) Does BD bisect AC ? Explain.
C) Does AC bisect BD ? Explain.
D) Connect points A, B, C, and D to construct quadrilateral ABCD.
E) Are there any congruent triangles formed by the diagonals of ABCD? Explain why or why not using
congruence postulates or theorems. Be specific.
F) Use your protractor to find the angles listed below. Based on your findings, fill in as many angles as possible.
m ABE 
m AEB 
G) Classify ABCD and summarize your findings about the diagonals.
m EBC 
C
4) Consider the diagram below to complete the following.
B
E
D
A
A) Find each of the following lengths to the nearest tenth of a centimeter.
AE =
CE =
AC =
BE =
DE =
BD =
B) Does BD bisect AC ? Explain.
C) Does AC bisect BD ? Explain.
D) Connect points A, B, C, and D to construct quadrilateral ABCD.
E) Are there any congruent triangles formed by the diagonals of ABCD? Explain why or why not using
congruence postulates or theorems. Be specific.
F) Use your protractor to find the angles listed below. Based on your findings, fill in as many angles as possible.
m ABE 
m AEB 
G) Classify ABCD and summarize your findings about the diagonals.
m EBC 
Algebra & Analytic Geometry
Unit 4 – Diagonals of Quadrilaterals
Name & Date
5) Consider the diagram below to complete the following.
B
E
A
C
D
A) Find each of the following lengths to the nearest tenth of a centimeter.
AE =
CE =
AC =
BE =
DE =
BD =
B) Does BD bisect AC ? Explain.
C) Does AC bisect BD ? Explain.
D) Connect points A, B, C, and D to construct quadrilateral ABCD.
E) Use your protractor to determine if AC  BD ? Explain.
F) Are there any congruent triangles formed by the diagonals of ABCD? Explain why or why not using
congruence postulates or theorems. Be specific.
G) Use your protractor to find the angles listed below. Based on your findings, fill in as many angles as
possible.
m ABE 
m AEB 
H) Classify ABCD and summarize your findings about the diagonals.
m EBC 
6)
A
D
E
C
B
A) Find each of the following lengths to the nearest tenth of a centimeter.
AE =
CE =
AC =
BE =
DE =
BD =
B) Does BD bisect AC ? Explain.
C) Does AC bisect BD ? Explain.
D) Connect points A, B, C, and D to construct quadrilateral ABCD.
E) Are there any congruent triangles formed by the diagonals of ABCD? Explain why or why not using
congruence postulates or theorems. Be specific.
F) Use your protractor to find the angles listed below. Based on your findings, fill in as many angles as possible
m BAE 
m AEB 
G) Classify ABCD and summarize your findings about the diagonals.
Algebra & Analytic Geometry
Unit 4 – Diagonals of Quadrilaterals
Name & Date
SUMMARY
Directions: Define the quadrilateral, then construct the diagonals and mark the diagram with ALL
congruent parts and parallel segments. Circle all relevant properties.
1) Square
A) At least one pair of parallel lines
B) Both pairs of opposite sides are parallel
C) Opposite sides are equal lengths
D) Four equal side lengths
E) Four right angles
F) Base angles are congruent
G) Two pairs of consecutive sides of equal lengths
H) Diagonals are perpendicular
I) Diagonals bisect each other (share the same midpoint)
J) Diagonals have equal lengths
K) Diagonals bisect each vertex angle
L) Consecutive angles are supplementary
M) Opposite angles are congruent
N) How many diagonals are considered a line of symmetry?
Neither
Both
Just One
Neither
Both
Just One
2) Rhombus
A) At least one pair of parallel lines
B) Both pairs of opposite sides are parallel
C) Opposite sides are equal lengths
D) Four equal side lengths
E) Four right angles
F) Base angles are congruent
G) Two pairs of consecutive sides of equal lengths
H) Diagonals are perpendicular
I) Diagonals bisect each other (share the same midpoint)
J) Diagonals have equal lengths
K) Diagonals bisect each vertex angle
L) Consecutive angles are supplementary
M) Opposite angles are congruent
N) How many diagonals are considered a line of symmetry?
3) Parallelogram
A) At least one pair of parallel lines
B) Both pairs of opposite sides are parallel
C) Opposite sides are equal lengths
D) Four equal side lengths
E) Four right angles
F) Base angles are congruent
G) Two pairs of consecutive sides of equal lengths
H) Diagonals are perpendicular
I) Diagonals bisect each other (share the same midpoint)
J) Diagonals have equal lengths
K) Diagonals bisect each vertex angle
L) Consecutive angles are supplementary
M) Opposite angles are congruent
N) How many diagonals are considered a line of symmetry?
Neither
Both
Just One
Neither
Both
Just One
4) Rectangle
A) At least one pair of parallel lines
B) Both pairs of opposite sides are parallel
C) Opposite sides are equal lengths
D) Four equal side lengths
E) Four right angles
F) Base angles are congruent
G) Two pairs of consecutive sides of equal lengths
H) Diagonals are perpendicular
I) Diagonals bisect each other (share the same midpoint)
J) Diagonals have equal lengths
K) Diagonals bisect each vertex angle
L) Consecutive angles are supplementary
M) Opposite angles are congruent
N) How many diagonals are considered a line of symmetry?
Algebra & Analytic Geometry
Unit 4 – Diagonals of Quadrilaterals
Name & Date
SUMMARY
5) Kite
A) At least one pair of parallel lines
B) Both pairs of opposite sides are parallel
C) Opposite sides are equal lengths
D) Four equal side lengths
E) Four right angles
F) Base angles are congruent
G) Two pairs of consecutive sides of equal lengths
H) Diagonals are perpendicular
I) Diagonals bisect each other (share the same midpoint)
J) Diagonals have equal lengths
K) Diagonals bisect each vertex angle
L) Consecutive angles are supplementary
M) Opposite angles are congruent
N) How many diagonals are considered a line of symmetry?
Neither
Both
Just One
6) Isosceles Trapezoid
A) At least one pair of parallel lines
B) Both pairs of opposite sides are parallel
C) Opposite sides are equal lengths
D) Four equal side lengths
E) Four right angles
F) Base angles are congruent
G) Two pairs of consecutive sides of equal lengths
H) Diagonals are perpendicular
I) Diagonals bisect each other (share the same midpoint)
J) Diagonals have equal lengths
K) Diagonals bisect each vertex angle
L) Consecutive angles are supplementary
M) Opposite angles are congruent
N) How many diagonals are considered a line of symmetry?
Neither
Both
Just One