Download Guided Notes - Triangles

Geometry
Guided Notes
Triangles
Name: ____________________________
Date: ___________________ Period: ____
Corollary – is a theorem that follows from a theorem that ___________________________________
_________________________________________________________________________
A
Triangle – 3 sided polygon (3 angles)
∆ - the symbol that represents a triangle;
B
C
Naming a Triangle – each vertex of the triangle will be labeled with a capital letter; use the triangle
symbol and each letter to name the triangle; _______________
Parts of a Triangle
4
9
B
3
8
A
Interior Angles:___________________
5
1
Exterior Angles: __________________
2
6
7 C
Vertex (Vertices) – each of the points, _____, ______, ______, is a vertex of the triangle.
Adjacent side – two sides that share a common vertex; _________________are adjacent sides
Opposite side – the side opposite a specified angle; ̅̅̅̅̅ is opposite ∡_______
Classified by their sides
A
1. Equilateral – a triangle with 3 congruent sides
C
B
Corollary for Equilateral Triangles -______________________________________________
__________________________________________________________________________
Geometry
Guided Notes
Triangles
Name: ____________________________
Date: ___________________ Period: ____
2. Scalene – a triangle that has no congruent sides
3. Isosceles – a triangle with at least 2 congruent sides; an isosceles triangle can have 3
A
congruent sides
B
C
Parts of an Isosceles Triangle
legs– if a triangle is isosceles with only 2 congruent sides, then the congruent sides are
A
referred to as the _____________,
base - the remaining non-congruent side
base angles - ______________________________.
C
B
Base Angles Theorem – If two sides of a triangle are congruent, then ______________
________________________________________________________________________
Theorem: If two angles of a triangle are congruent, then _______________________
________________________________________________________________________
Classified by their angles
1. Acute- a triangle with all _________ angles
2. Obtuse – a triangle with exactly _______ __________ angle
3. Equiangular – an acute triangle in which __________________________
Geometry
Guided Notes
Triangles
Name: ____________________________
Date: ___________________ Period: ____
Corollary (Equiangular): If a triangle is equiangular, then it is also _____________________.
4. Right – a triangle with exactly one right angle
hypotenuse – if a triangle is a right triangle, then the side opposite the right angle is
called the hypotenuse and the sides _________________________________________.
ONE 90° ANGLE AND 2 ACUTE ANGLES!
Theorem: The acute angles of a right triangle are _______________________________.
Example:
x
2x
Marking the Triangle
Equilateral
Equiangular
Isosceles
Scalene
Right
Geometry
Guided Notes
Triangles
Name: ____________________________
Date: ___________________ Period: ____
Solving Triangles Problems
Example #1: ΔABC is an isosceles triangle with ̅̅̅̅
triangle is equilateral.
̅̅̅̅ . Solve for x, then decide if the
A
2x - 1
4x - 2
C
B
x+1
Example #2:
Example #3:
A
A
3x - 5
15
2x + 1
C
B
B
25
C
Triangle Sum Theorem – the sum of the measures of the interior angles of a triangle is __________.
Example #1: Find the measure of ∡1, ∡2, and ∡3.
28° 51°
1
42°
2 3
Example #2: Solve for x and find the measure of each angle.
5x + 5
6x
7x - 5
Geometry
Guided Notes
Triangles
Name: ____________________________
Date: ___________________ Period: ____
Example #3: Solve for x.
2x + 3
110°
Example #4: Find x and y.
50°
y
x
Exterior Angle Theorem - the measure of an exterior angle of a triangle is equal to the sum of the
measures of the __________________________________________________________________
A
1
B
C
Example #1:
A
55°
40°
B
1
C
Geometry
Guided Notes
Triangles
Name: ____________________________
Date: ___________________ Period: ____
Example #2:
A
65°
x°
2x + 10
B
C
Example #3:
A 11x - 3
2x + 4
8x + 1
B
C
Exterior Angle Inequality – the measure of an exterior angle of a triangle is ____________________ the
measure of either of the two remote (nonadjacent) interior angles
A
1
B
C
Third Angles Theorem – if two angles of a triangle are _______________ to two angles of second
triangle, then the ______________are also ______________________.
Geometry
Guided Notes
Triangles
Solve for each missing angle.
Name: ____________________________
Date: ___________________ Period: ____