Download Section 4.7: Isosceles and Equilateral Triangles

Section 4.7: Isosceles and
Equilateral Triangles
Understand the relationship between
Sides and Angles in Isosceles and
Equilateral Triangles and be able to
use that relationship to solve
problems.
Vocabulary of Isosceles Triangles
Vertex Angle
Leg
Leg
Base Angles
Theorem 4.7: Base Angles Theorem.
• If two Sides of a triangle are
congruent, then the Angles
opposite them are Congruent.
OR
• If the Legs of an Isosceles
Triangle are congruent then
the Base Angles must be
congruent.
A
Leg
Leg
Base Angles
If 𝑨𝑩 ≅ 𝑨𝑪, then ∠𝑩 ≅ ∠𝑪
B
C
Theorem 4.7: Base Angles Theorem
J
Proof
Statements
1. 𝐽𝐾 ≅ 𝐽𝐿
2. M is Midpoint of
𝐾𝐿
3. Draw 𝐽𝑀
K
L
4. 𝐾𝑀 ≅ 𝐿𝑀
Given: ∆𝐽𝐾𝐿, 𝐽𝐾 ≅ 𝐽𝐿 5. 𝐽𝑀 ≅ 𝐽𝑀
Prove: ∠𝑘 ≅ ∠𝑙
6. ∆𝐽𝐾𝑀 ≅ ∆𝐽𝐿𝑀
7. ∠𝐾 ≅ ∠𝐿
Reasons
1. Given
2. Def. of
Midpoint
3. 2 points
determine a line
4. Def. of Midpoint
5. Reflexive
Property
6. SSS
7. CPCTC
Theorem 4.8: Converse Base Angles
Theorem.
• If two Angles of a triangle are
congruent, then the Sides
opposite them are Congruent.
OR
• If the Base Angles of an
Isosceles Triangle are
congruent then the Legs must
be congruent.
A
Leg
Leg
Base Angles
If ∠𝑩 ≅ ∠𝑪, then 𝑨𝑩 ≅ 𝑨𝑪
B
C
This is the Transamerica Building.
You need to reproduce the pyramid on
the top of the building to create a logo
for the Transamerica Corp. The
information you have been given is that
the angle at the lower right hand corner
of the pyramid is approximately 85°.
In order to create a logo that visually
matches the building you will need to
find the measure of the other two
angles.
Describe your method:
Equilateral Triangles
Base Angles Corollary
• If two congruent sides
means two congruent
angles, then three
congruent sides must
mean three congruent
angles
Corollaries: Equilateral Triangles
• Corollary to the Base
Angles Theorem: If a
Triangle is equilateral, then
it is equiangular.
Why must this be true?
• Corollary to the Converse
Base Angles Theorem: If a
Triangle is equiangular,
then it is equilateral.
Homework
4.7 p.267 # 1,3,6,9,12,15,18,21