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Isosceles and Equilater
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Section 4-6Isosceles and Equilateral Triangles
Wednesday, February 8, 2012
Essential Questions
❖ How do you use properties of isosceles triangles?
❖ How do you use properties of equilateral triangles?
Wednesday, February 8, 2012
Vocabulary1. Legs of an Isosceles Triangle:
2. Vertex Angle:
3. Base Angles:
Wednesday, February 8, 2012
Vocabulary1. Legs of an Isosceles Triangle: The two congruent sides
of an isosceles triangle
2. Vertex Angle:
3. Base Angles:
Wednesday, February 8, 2012
Vocabulary1. Legs of an Isosceles Triangle: The two congruent sides
of an isosceles triangle
2. Vertex Angle: The included angle between the legs of an isosceles triangle
3. Base Angles:
Wednesday, February 8, 2012
Vocabulary1. Legs of an Isosceles Triangle: The two congruent sides
of an isosceles triangle
2. Vertex Angle: The included angle between the legs of an isosceles triangle
3. Base Angles: The angles formed between each leg and the base of an isosceles triangle
Wednesday, February 8, 2012
Theorems and CorollariesTheorem 4.10 - Isosceles Triangle Theorem:
Theorem 4.11 - Converse of Isosceles Triangle Theorem:
Corollary 4.3 - Equilateral Triangles:
Corollary 4.4 - Equilateral Triangles:
Wednesday, February 8, 2012
Theorems and CorollariesTheorem 4.10 - Isosceles Triangle Theorem: If two sides
of a triangle are congruent, then the angles opposite those sides are congruent
Theorem 4.11 - Converse of Isosceles Triangle Theorem:
Corollary 4.3 - Equilateral Triangles:
Corollary 4.4 - Equilateral Triangles:
Wednesday, February 8, 2012
Theorems and CorollariesTheorem 4.10 - Isosceles Triangle Theorem: If two sides
of a triangle are congruent, then the angles opposite those sides are congruent
Theorem 4.11 - Converse of Isosceles Triangle Theorem:If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Corollary 4.3 - Equilateral Triangles:
Corollary 4.4 - Equilateral Triangles:
Wednesday, February 8, 2012
Theorems and CorollariesTheorem 4.10 - Isosceles Triangle Theorem: If two sides
of a triangle are congruent, then the angles opposite those sides are congruent
Theorem 4.11 - Converse of Isosceles Triangle Theorem:If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Corollary 4.3 - Equilateral Triangles: A triangle is equilateral IFF it is equiangular
Corollary 4.4 - Equilateral Triangles:
Wednesday, February 8, 2012
Theorems and CorollariesTheorem 4.10 - Isosceles Triangle Theorem: If two sides
of a triangle are congruent, then the angles opposite those sides are congruent
Theorem 4.11 - Converse of Isosceles Triangle Theorem:If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Corollary 4.3 - Equilateral Triangles: A triangle is equilateral IFF it is equiangular
Corollary 4.4 - Equilateral Triangles: Each angle of an equilateral triangle measures 60°
Wednesday, February 8, 2012
Example 1a. Name two unmarked congruent angles.
b. Name two unmarked congruentsegments
Wednesday, February 8, 2012
Example 1a. Name two unmarked congruent angles.
b. Name two unmarked congruentsegments
Wednesday, February 8, 2012
Example 1a. Name two unmarked congruent angles.
b. Name two unmarked congruentsegments
Wednesday, February 8, 2012
Example 2Find each measure.
a.
b. PR
Wednesday, February 8, 2012
Example 2Find each measure.
180 - 60a.
b. PR
Wednesday, February 8, 2012
Example 2Find each measure.
180 - 60 = 120a.
b. PR
Wednesday, February 8, 2012
Example 2Find each measure.
180 - 60 = 120 120 ÷ 2a.
b. PR
Wednesday, February 8, 2012
Example 2Find each measure.
180 - 60 = 120 120 ÷ 2 = 60a.
b. PR
Wednesday, February 8, 2012
Example 2Find each measure.
180 - 60 = 120 120 ÷ 2 = 60= 60°
a.
b. PR
Wednesday, February 8, 2012
Example 2Find each measure.
180 - 60 = 120 120 ÷ 2 = 60= 60°
a.
b. PR
Since all three angles will be 60°, this is an equilateral triangle, so PR = 5 cm.
Wednesday, February 8, 2012
Example 3Find the value of each variable.
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0Now what?
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0Now what?
4x − 8 = 60
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0Now what?
4x − 8 = 60+ 8 + 8
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0Now what?
4x − 8 = 60+ 8 + 84x = 68
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0Now what?
4x − 8 = 60+ 8 + 84x = 68
44
Wednesday, February 8, 2012
Example 3Find the value of each variable.
6y + 3 = 8y − 5− 6y − 6y
3 = 2y − 5+ 5 + 5
8 = 2y22
y = 4
4x − 8 = 4x − 8− 4x − 4x+ 8 + 8
0 = 0Now what?
4x − 8 = 60+ 8 + 84x = 68
44x = 17
Wednesday, February 8, 2012
Check Your Understanding
Check out p. 287 #1-8 and see if you have an idea of what to do with these problems
Wednesday, February 8, 2012
Problem Set
Wednesday, February 8, 2012
Problem Set
p. 287 #9-31 odd (skip 27), 47, 56, 61
“We have, I fear, confused power with greatness.”- Stewart L. Udall
Wednesday, February 8, 2012
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