int math 2 section 5-4 1011
DESCRIPTION
Properties of TrianglesTRANSCRIPT
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Section 5-4Properties of Triangles
Tue, Jan 25
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Essential Questions
How do you classify triangles according to their sides and angles?
How do you identify and use properties of triangles?
Where you’ll see this:
Travel, interior design, navigation
Tue, Jan 25
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Vocabulary
1. Triangle:
2. Vertex:
3. Congruent Sides:
4. Congruent Angles:
5. Exterior Angle:
6. Base Angles:
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex:
3. Congruent Sides:
4. Congruent Angles:
5. Exterior Angle:
6. Base Angles:
Tue, Jan 25
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex: The point where two sides meet3. Congruent Sides:
4. Congruent Angles:
5. Exterior Angle:
6. Base Angles:
Tue, Jan 25
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex: The point where two sides meet3. Congruent Sides: Sides that are the same length4. Congruent Angles:
5. Exterior Angle:
6. Base Angles:
Tue, Jan 25
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex: The point where two sides meet3. Congruent Sides: Sides that are the same length4. Congruent Angles: Angles with the same measure5. Exterior Angle:
6. Base Angles:
Tue, Jan 25
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex: The point where two sides meet3. Congruent Sides: Sides that are the same length4. Congruent Angles: Angles with the same measure5. Exterior Angle: The angle formed by extending a side outside of the
triangle
6. Base Angles:
Tue, Jan 25
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex: The point where two sides meet3. Congruent Sides: Sides that are the same length4. Congruent Angles: Angles with the same measure5. Exterior Angle: The angle formed by extending a side outside of the
triangle
6. Base Angles:DF
R
P
Tue, Jan 25
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Vocabulary
1. Triangle: A shape with three sides and three angles2. Vertex: The point where two sides meet3. Congruent Sides: Sides that are the same length4. Congruent Angles: Angles with the same measure5. Exterior Angle: The angle formed by extending a side outside of the
triangle
6. Base Angles: In an isosceles triangle, the angles that are opposite of the congruent sides
DF
R
P
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B
A
C
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B
A
C
Vertices:
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B
A
C
Vertices: A, B, C
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B
A
C
Vertices: A, B, C
Sides:
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B
A
C
Vertices: A, B, C
Sides: AB, BC , AC
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B
A
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles:
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B
A
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles: ∠A,∠B,∠C
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B
A
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles: ∠A,∠B,∠Cor
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B
A
C
Vertices: A, B, C
Sides: AB, BC , AC
Angles: ∠A,∠B,∠C
∠BAC ,∠ABC ,∠ACBor
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Triangle Vocabulary
Scalene Triangle:
Acute Triangle:
Isosceles Triangle:
Obtuse Triangle:
Right Triangle:
Equilateral Triangle:
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Triangle Vocabulary
Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures
Acute Triangle:
Isosceles Triangle:
Obtuse Triangle:
Right Triangle:
Equilateral Triangle:
Tue, Jan 25
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Triangle Vocabulary
Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures
Acute Triangle: All three angles are less than 90 degrees
Isosceles Triangle:
Obtuse Triangle:
Right Triangle:
Equilateral Triangle:
Tue, Jan 25
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Triangle Vocabulary
Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures
Acute Triangle: All three angles are less than 90 degrees
Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides
Obtuse Triangle:
Right Triangle:
Equilateral Triangle:
Tue, Jan 25
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Triangle Vocabulary
Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures
Acute Triangle: All three angles are less than 90 degrees
Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides
Obtuse Triangle:
Right Triangle:
Equilateral Triangle: All sides are congruent, as are all angles
Tue, Jan 25
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Triangle Vocabulary
Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures
Acute Triangle: All three angles are less than 90 degrees
Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides
Obtuse Triangle: Has one angle that is greater than 90 degrees
Right Triangle:
Equilateral Triangle: All sides are congruent, as are all angles
Tue, Jan 25
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Triangle Vocabulary
Scalene Triangle: A triangle where all three sides have different lengths and all three angles have different measures
Acute Triangle: All three angles are less than 90 degrees
Isosceles Triangle: Has two congruent sides and two congruent angles; The congruent angles are opposite of the congruent sides
Obtuse Triangle: Has one angle that is greater than 90 degrees
Right Triangle: Had a right angle; The side opposite of the right angle is the hypotenuse (longest side) and the other sides are the legs
Equilateral Triangle: All sides are congruent, as are all angles
Tue, Jan 25
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Properties of Triangles
Tue, Jan 25
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Properties of Triangles
1. The sum of the angles in a triangle is 180 degrees
Tue, Jan 25
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Properties of Triangles
1. The sum of the angles in a triangle is 180 degrees
2. If you add two sides of a triangle, the sum will be bigger than the length of the third side
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Properties of Triangles
1. The sum of the angles in a triangle is 180 degrees
2. If you add two sides of a triangle, the sum will be bigger than the length of the third side
3. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle
Tue, Jan 25
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Properties of Triangles
1. The sum of the angles in a triangle is 180 degrees
2. If you add two sides of a triangle, the sum will be bigger than the length of the third side
3. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle
4. The exterior angle formed at one vertex equals the sum of the other two interior angles
Tue, Jan 25
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Properties of Triangles
1. The sum of the angles in a triangle is 180 degrees
2. If you add two sides of a triangle, the sum will be bigger than the length of the third side
3. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle
4. The exterior angle formed at one vertex equals the sum of the other two interior angles
5. If two sides are congruent, then the angles opposite those sides are congruent
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1 FG
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2
FG
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2
FG
HG
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
FG
HG
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
FG
HG FH
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
#1
FG
HG FH
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
#1
FG
HG FH
FG
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
#1#2
FG
HG FH
FG
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
#1#2
FG
HG FH
FG
FE
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
#1#2
#3
FG
HG FH
FG
FE
Tue, Jan 25
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Example 1
For the two triangles, list the sides from shortest to longest.
F
G
E
H
m∠FHG =50° m∠HGF =75° m∠GFH =55°
m∠GFE =90° m∠FEG = 40° m∠EGF =50°
#1
#2#3
#1#2
#3
FG
HG FH
FG
FE
GE
Tue, Jan 25
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Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
DF
R
P
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
m∠RDP =180−m∠RDF
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
=180−57 m∠RDP =180−m∠RDF
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
=180−57 m∠RDP =180−m∠RDF
m∠RDP =123°Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
=180−57 m∠RDP =180−m∠RDF
m∠RDP =123°
m∠RPD =180−m∠RDP −m∠DRP
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
=180−57 m∠RDP =180−m∠RDF
m∠RDP =123°
m∠RPD =180−m∠RDP −m∠DRP m∠RPD =180−123−24
Tue, Jan 25
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DF
R
P
Example 2
In the figure, m∠RFD =33°, m∠FRD =90°, and m∠DRP =24°.Find the measures of the other angles.
m∠RDF =180−m∠DRF −m∠RFD m∠RDF =180−33−90
m∠RDF =57°
=180−57 m∠RDP =180−m∠RDF
m∠RDP =123°
m∠RPD =180−m∠RDP −m∠DRP m∠RPD =180−123−24
m∠RPD =33°
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p. 208 #1-33 odd
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