Section 5-4Properties of Triangles

Tue, Jan 25

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

Vocabulary

1. Triangle:

2. Vertex:

3. Congruent Sides:

4. Congruent Angles:

5. Exterior Angle:

6. Base Angles:

Tue, Jan 25

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

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

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

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

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

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

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

Tue, Jan 25

B

A

C

Tue, Jan 25

B

A

C

Vertices:

Tue, Jan 25

B

A

C

Vertices: A, B, C

Tue, Jan 25

B

A

C

Vertices: A, B, C

Sides:

Tue, Jan 25

B

A

C

Vertices: A, B, C

Sides: AB, BC , AC

Tue, Jan 25

B

A

C

Vertices: A, B, C

Sides: AB, BC , AC

Angles:

Tue, Jan 25

B

A

C

Vertices: A, B, C

Sides: AB, BC , AC

Angles: ∠A,∠B,∠C

Tue, Jan 25

B

A

C

Vertices: A, B, C

Sides: AB, BC , AC

Angles: ∠A,∠B,∠Cor

Tue, Jan 25

B

A

C

Vertices: A, B, C

Sides: AB, BC , AC

Angles: ∠A,∠B,∠C

∠BAC ,∠ABC ,∠ACBor

Tue, Jan 25

Triangle Vocabulary

Scalene Triangle:

Acute Triangle:

Isosceles Triangle:

Obtuse Triangle:

Right Triangle:

Equilateral Triangle:

Tue, Jan 25

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

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

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

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

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

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

Properties of Triangles

Tue, Jan 25

Properties of Triangles

1. The sum of the angles in a triangle is 180 degrees

Tue, Jan 25

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

Tue, Jan 25

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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°

Tue, Jan 25

Problem Set

Tue, Jan 25

Problem Set

p. 208 #1-33 odd

“Change your thoughts and you change your world.” - Norman Vincent Peale

Tue, Jan 25