Download Mathematician: Date: Core-Geometry: 4.1 Triangle Sum and 4.2

Mathematician: _________________________
Date: _______________
Core-Geometry: 4.1 Triangle Sum
and 4.2 Congruence and Triangles
Warm-up:
1. Determine the distance between (10, 50) and (40, 90).
2. Determine the slope between (-8, -3) and (-12, -15).
Constructions Review
1. Copy the given angle.
2. If the provided angle has x degrees, construct another angle that has ½x degrees.
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4.1 Applying Triangle Sum Properties
A ______________ is a polygon with three sides. A ________________with vertices
A, B, and C is called _________________ _______ or using symbols ____ ______.
Triangles can be classified by their _______________.
No congruent sides
At least 2 congruent sides
3 congruent sides
Triangles may also be classified by their ______________.
3 acute angles
1 right angle
1 obtuse angle
3 congruent angles
Note: An equilateral triangle can also be classified as ___________________.
Example 1
Classify the triangles by sides and angles:
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When the sides of a _______________ are extended, other angles are formed. The
__________ angles are the _______________ angles. The angles formed by extending
the lines form _______________ pairs. These angles are called __________________
angles.
The Triangle ___________Theorem: The ________ of the measures of the
______________ angles of a triangle is _____________.
Using what we know about linear pairs, we can find an important property for the
measure of an exterior angle.
The measure of an __________________ angle of a triangle is ____________ to the
_____ of the measures of the two ____________________ _________________ angles.
Example 2
Write equations and solve to find the variables below. Then find the measure of each
missing angle.
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4.2 Applying Congruence and Triangles
Two __________________figures are congruent if they have _______________the same
___________ and ____________________. In two ____________________figures, all
the _____________of one figure are _________________to the
__________________________ parts of the other _______________. When you write a
congruence statement for two polygons, it is important to list the corresponding
_______________ is the same __________.
What congruence statements can be written for the triangles below?
Example 1
Find the value of the variable if Polygon ABCDE @ Polygon FGHIJ
Example 2
Can you tell if the triangles below are congruent? Why?
If they are congruent, write congruence statements for the triangles and all of the
corresponding parts.
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Third Angles: Using what you know about the sum of angle measures, what do you
notice about the missing angles in the two triangles below?
If two angles of one triangle are __________________ to two angles of another triangle,
then the third angles are also ___________________.
Example 3
Find the value of x.
(a)
(b)
Hmwk 3.1
p.228 Ex 4.2 # 5-10, 11, 13, 15, 19, 21
p.221 Ex 4.1 # 1-6, 11, 15, 17, 19, 21-26, 27, 31, 33
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