Modern Geometry – Review Packet #2 Chapters 5 - 7
Chapter 5 – Relationships within Triangles
Theorem 5-1 – Traingle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is __________ to the third side, and is
_________ its length.
Mark the figure shown below to illustrate the Triangle Midsegment Theorem:
Use the Triangle Midsegment Theorem to solve the following problems.
1.
2.
4.
5.
3.
1
Modern Geometry – Review Packet #2 Chapters 5 - 7
You should be able to define the following terms for a triangle:
Perpendicular Bisector:
Altitude:
Angle Bisector:
Median:
Based on these definitions, label the following for the diagram shown below.
A perpendicular bisector:
An angle bisector:
A median:
An altitude:
Inequalities in Triangles
Theorem 5-10: If two sides of a triangle are not congruent, then the ______________ angle lies opposite the longer
side.
Theorem 5-11: If two angles of a triangle are not congruent, then the __________ side lies opposite the larger angle.
2
Modern Geometry – Review Packet #2 Chapters 5 - 7
Theorem 5-12: Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle is
______________ than the length of the third side.
Use the inequalities in triangles theorems to solve the following problems.
List the angles of each triangle in order from largest to smallest.
List the sides of each triangle in order from shortest to longest.
7.) One side of a triangle has a length of 3. What could be the lengths of the other two sides?
a.) 12 and 12
b.) 9 and 15
c.) 3 and 9
d.) 18 and 12
3
Modern Geometry – Review Packet #2 Chapters 5 - 7
Chapter 6 – Quadrilaterals
List ALL the properties of the following quadrilaterals. Then mark the diagram.
Figure
Parallelogram
Diagram
Rectangle
Rhombus
Square
Trapezoid
Isoceles Trapezoid
Kite
4
Modern Geometry – Review Packet #2 Chapters 5 - 7
For each property listed below list all the shapes that share that property. You shape choices are:
parallelogram, rectangle, rhombus, square, isosceles trapezoid, and kite.
a. Diagonals are congruent _______________________________________________________________
b. All sides are congruent _________________________________________________________________
c. Diagonals are perpendicular __________________________________________________________
d. Opposite sides are parallel ____________________________________________________________
e. All angles are right angles _____________________________________________________________
f.
Consecutive angles are supplementary ___________________________________________________
g. Diagonals bisect each other _____________________________________________________________
h. There is only one side of parallel sides ________________________________________________
i.
Has two pairs of adjacent sides congruent and no opposite sides congruent.
_____________________________________________________________
j.
Each diagonal bisects opposite angles ____________________________________________________
Use the properties of a parallelogram to find the coordinates of the points.
Use the properties of quadralaterals to solve for the missing variables.
5
Modern Geometry – Review Packet #2 Chapters 5 - 7
5.) LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 10x – 16 and MP = 4x + 2.
6.) Find the value of x in the kite shown below:
6
Modern Geometry – Review Packet #2 Chapters 5 - 7
Chapter 7 Area
Figure
The area of a rectangle is the product of its _________
and __________.
Diagram & Area Formula
The area of a parallelogram is the product of a
____________ and the corresponding _____________
The area a triangle is __________ the product of a
_________ and the corresponding height.
The area of a trapezoid is _________ the product of the
__________ and the _________ of the bases.
The area of a rhombus or a kite is ___________ the
product of the lengths of the ______________.
Find the area of each figure. If your answer is not an integer, leave it in simplest radical form.
7
Modern Geometry – Review Packet #2 Chapters 5 - 7
5.) In the figure shown, all angles are right angles.
The Pythagorean Theorem and its Converse
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the lengths of the
hypotenuse.
_________________________________________
8
Modern Geometry – Review Packet #2 Chapters 5 - 7
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of
the other two sides, the triangle is ____________________.
If _________________________, the triangle is ___________________.
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the
other two sides, the triangle is ______________________.
If ______________________________, the triangle is acute.
Find the value of each variable. If your answer is not an integer, leave it in simplest radical form.
4. For the rectangle below, find the length of its diagonal.
5.) A square has an area of 36 square inches. Find the length of the diagonal.
6.) The lengths of the sides of a triangle are given. Classify each triangle as acute, obtuse, or right.
a.) 7, 8, 9
b.) 15, 36, 39
c.) 10, 12, 16
9
Modern Geometry – Review Packet #2 Chapters 5 - 7
Special Right Triangles
Label the generic sides of the special triangles shown below.
Use the properties of special triangles to find the value of each variable, If your answer is not an integer, leave it in
its simplest radical form.
Circles:
The area of a circle is ______________________
The circumference of a circle is ______________________
10
Modern Geometry – Review Packet #2 Chapters 5 - 7
Use the formulas for area of a circle, circumference of a circle, arc length, and area of a sector to solve the following
problems.
4.) The circle below has a diameter of 46 units. Arc AB on the circle has an arc length of 24 units. What is the
measure of AOB ?
Find the area of the sectors shown.
11