4.6 isosceles triangles
DESCRIPTION
4.6 Isosceles Triangles. Objectives. Use properties of isosceles triangles Use properties of equilateral triangles. Properties of Isosceles Triangles. The formed by the ≅ sides is called the vertex angle . The two ≅ sides are called legs . The third side is called the base . - PowerPoint PPT PresentationTRANSCRIPT
4.6 Isosceles Triangles
Objectives
Use properties of isosceles triangles
Use properties of equilateral triangles
Properties of Isosceles Triangles
The formed by the ≅ sides is called the vertex angle.
The two ≅ sides are called legs. The third side is called the base.
The two s formed by the base and the legs are called thebase angles.
leg leg
base
vertex
Isosceles Triangle Theorem
Theorem 4.9If two sides of a ∆ are ≅, then the s opposite those sides are ≅ (if AC ≅ AB, then B ≅ C). A
B C
Write a two-column proof.
Given:
Prove:
Example 1:
Proof:
ReasonsStatements
3. Def. of Isosceles 3. ABC and BCD are isosceles triangles
1. Given1.
6. 6. Substitution
5. 5. Given
4. 4. Isosceles Theorem
2. Def. of Segments2.
Example 1:
Write a two-column proof.
Given: .
Prove:
Your Turn:
Proof:
ReasonsStatements
1. Given
3. Isosceles Theorem
2. Def. of Isosceles Triangles
1.
2. ADB is isosceles.
3.
4.
5.
4. Given
5. Def. of Midpoint
6. SAS
7. 7. CPCTC
6. ABC ADC
Your Turn:
The Converse of Isosceles Triangle Theorem
Theorem 4.10
If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).
Answer:
Name two congruent angles.
Example 2:
Answer:
Name two congruent segments.
By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So,
Example 2:
a. Name two congruent angles.
Answer:
Answer:
b. Name two congruent segments.
Your Turn:
Properties of Equilateral ∆s
Corollary 4.3A ∆ is equilateral iff it is equiangular.
Corollary 4.4Each of an equilateral ∆ measures 60°.
Since the angle was bisected,Each angle of an equilateral triangle measures 60°.
EFG is equilateral, and bisects bisectsFind and
Example 3a:
Answer:
Add.
Exterior Angle Theorem
Substitution
is an exterior angle of EGJ.
Example 3a:
Subtract 75 from each side.
Linear pairs are supplementary.
Substitution
Answer: 105
EFG is equilateral, and bisects bisectsFind
Example 3b:
a. Find x.
b.
Answer: 90
Answer: 30
ABC is an equilateral triangle. bisects
Your Turn:
Assignment
Geometry:Pg. 219 #9 – 28, 35 - 37
Pre-AP Geometry: Pg. 219 #9 – 30, 35 – 37, & 40