M3: Triangles
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Academic
Pre-Algebra
Geometry Notes
10.1 to 10.4
Name___________________ Pd.____
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Sections 10.1 to 10.2
List of Vocabulary Words
Triangle Notes:
 Acute triangle
 Right triangle
 Obtuse triangle
 Equiangular triangle
 Isosceles triangle
 Scalene triangle
 Equilateral triangle
Section 10.2:
 Polygon
 Regular polygon
 Convex
 Concave
Sections 10.2 to 10.4
List of Vocabulary Words
Lines Notes:
 Parallel lines
 Perpendicular lines
 Skew lines
Section 10.3:
 Trapezoid
 Parallelogram
 Rhombus
 Rectangle
 Square
 Diagonal of a polygon
Section 10.4:
 Circle
 Center
 Radius
 Diameter
 Circumference
 Area of a circle
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Triangles
Learning Goal: We will prepare for solving problems that involve triangles.
SUM OF ANGLE MEASURES IN A TRIANGLE:
**The sum of the angle measures in any triangle is __________.
Example 1: Find the value of x.
CLASSIFYING TRIANGLES BY ANGLE MEASURES
Example 2: Classify the triangle by its angle measures.
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CLASSIFYING TRIANGLES BY SIDE LENGTHS
Example 3: Classify the triangle by its side lengths.
14 in.
16 in.
EXTRA PRACTICE:
11 in.
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Section 10.1: Triangles
Learning Goal: We will solve problems involving triangles.
Example 1: Classifying a Triangle by Angle Measures
Find the value of x. Then classify the triangle by the angle measures.
ON YOUR OWN:
In the diagram, mU  23 and mS  mU . Find mS and mT . Then
classify ΔSTU by its angle measures.
T
S
U
Example 2: Finding Unknown Side Lengths
The perimeter of an isosceles triangle is 35 inches. The length of the
shortest side is 4 inches less than the length of each of the other two
sides. Find the lengths of all three sides of the triangle.
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ON YOUR OWN:
Example 3: Finding Angle Measures Using a Ratio
The ratio of the angle measures of a triangle is 7 : 9 : 20. Find the
angle measures. Then classify the triangle by its angle measures.
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ON YOUR OWN:
EXTRA PRACTICE:
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Triangle Inequality Theorem
Learning Goal: We will determine whether three segments can form a triangle.
Triangle Inequality Theorem:
The sum of the lengths of any _____ sides of a triangle is greater
than the length of the third side.
**All three conditions must be true for the sides to form a triangle.
**As soon as you know that the sum of 2 sides is less than (or equal to)
the measure of a third side, then you know that the sides do not make
up a triangle.
Example 1: Using the Triangle Inequality Theorem
Do segments with lengths 10, 4, and 3 form a triangle?
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Check whether it is possible to have a triangle with the given side
lengths: 7, 9, 13.
ON YOUR OWN:
Check whether the given side lengths form a triangle: 4, 8, 15.
Example 2: Identifying the Number of Triangles
How many triangles exist with the given side lengths?
7 inches, 7 inches, 7 inches
How many triangles exist with the given side lengths?
3 cm, 5 cm, 9 cm
ON YOUR OWN:
How many triangles exist with the given side lengths?
12 inches, 15 inches, 18 inches
Example 3: Types of Triangles
Two sides of an isosceles triangle measure 3 and 7. Which of the
following could be the measure of the third side?
9, 7, or 3
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Section 10.2: Polygons and Quadrilaterals
Learning Goal: We will classify polygons and quadrilaterals.
Vocabulary:
 Polygon – a closed plane figure whose sides are segments and
intersect only at their endpoints
 Regular polygon – a polygon whose sides all have the same length
and whose angles all have the same measure
 Convex – a polygon where a segment joining any two interior
points lies completely within the polygon
 Concave – a polygon that is not convex
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Common 2-Dimensional Shapes
Example 1: Identifying and Classifying Polygons
ON YOUR OWN:
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QUADRILATERALS:
Example 2: Classifying Quadrilaterals
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ON YOUR OWN:
 Diagonal of a polygon – a segment that joins two vertices of the
polygon that are not adjacent
***The sum of the angle measures in a quadrilateral is ____________.
Example 3: Finding an Unknown Angle Measure
ON YOUR OWN:
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Parallel, Perpendicular, and Skew Lines
Learning Goal: We will prepare for solving problems that involve parallel and
perpendicular lines.
PARALLEL LINES:
 Parallel lines –
Example 1: Name one pair of parallel lines that lie in plane P.
PERPENDICULAR LINES:
 Perpendicular lines –
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Example 2: Name two lines that are perpendicular.
SKEW LINES:
 Skew lines –
Example 3: Name two lines that are skew.
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EXTRA PRACTICE:
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Section 10.3: Areas of Parallelograms and Trapezoids
Learning Goal: We will find the areas of parallelograms and trapezoids.
Vocabulary:
 Base of a parallelogram – the length of any side of a parallelogram
 Height of a parallelogram – the perpendicular distance between
the side whose length is the base and the opposite side.
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Example 1: Finding the Area of a Parallelogram
The height of a parallelogram is 12 inches. The base is two thirds of
the height. Find the area of the parallelogram.
ON YOUR OWN:
Find the area of the parallelogram.
 Bases of a trapezoid – the lengths of the parallel sides of the
trapezoid
 Height of a trapezoid – the perpendicular distance between the
sides whose lengths are the bases.
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Example 2: Finding the Area of a Trapezoid
ON YOUR OWN:
Find the area of the trapezoid.
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Example 3: Finding an Unknown Length
The bases of a trapezoid are 11 inches and 17 inches. The area of the
trapezoid is 56 square inches. Find the height.
ON YOUR OWN:
Example 4: Using Area of Trapezoids
You are building an L-shaped desk for
your room. The dimensions of the
desktop are shown. Find the area of the
desktop.
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Section 10.4: Circumference and Area of a Circle
Learning Goal: We will find circumference and areas of circles.
Vocabulary:
 Circle – all points in a plane that are the same distance from a
fixed point
 Center –the point inside the
circle that is the same
distance from all the points
on the circle
 Radius –
 Diameter –
 Circumference –
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Example 1: Finding the Circumference of a Circle
The supercollider ring of the physics research facility CERN in
Switzerland is a circle with a radius of about 4.25 kilometers. Find the
circumference of the ring to the nearest kilometer.
ON YOUR OWN:
Example 2: Finding the Radius of a Circle
a. The circumference of a
b. The circumference of a
circle is 500 feet. Find the
circle is 70 inches. Find the
radius of the circle to the
radius of the circle to the
nearest foot.
nearest inch.
ON YOUR OWN:
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Example 3: Finding the Area of a Circle
a. The diameter of a circle is
b. Find the area of the circle to
54 centimeters. Find the
the nearest square foot.
area of the circle to the
nearest square centimeter.
ON YOUR OWN:
Example 4: Finding the Radius of a Circle
The area of a circle is 250 square inches. Find the radius of the circle
to the nearest inch.
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ON YOUR OWN:
Example 5: Finding the Area of a Figure
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