Transcript area of ​​a triangle isosceles

Objectives:
- Use congruence of triangles to conclude congruence of
corresponding parts.
- Develop and use the Isosceles Triangle Theorem
Warm-Up:
Statements
Given: ABCD is
a rectangle.
Prove: ΔABC & ΔCDA
are ≅ by ASA
A
B
D
C
Reasons
An isosceles triangle is a
triangle with at least two
congruent sides. The two
congruent sides are known as
the legs of the triangle, and
the remaining side is known
as the base. The angles
whose
vertices
are
the
endpoints of the base are
known as base angles, and
the angle opposite the base
is known as the vertex angle.
VERTEX ANGLE
LEGS
BASE ANGLES
BASE
Isosceles Triangle Theorem:
If two sides of a triangle are congruent, then
the angles opposite those sides are congruent.
Converse of the Isosceles Triangle Theorem:
If two angles of a triangle are congruent, then
the sides opposite those angles are congruent.
Corollary:
A corollary of a theorem is an additional
theorem that can easily be derived from the
original theorem.
Once the theorem is known, the corollary
should seem obvious.
A corollary can be used as a reason in a
proof, just like a theorem or postulate.
Corollary:
The measure of each
angle of an equilateral
triangle is 𝟔𝟎𝟎 .
Corollary:
The bisector of the vertex
angle of an isosceles triangle
is the perpendicular bisector
of the base.
Examples:
What is the length of BA?
B
𝟑𝟎𝟎
A
𝟔𝟎
𝟎
𝟏𝟎
X
𝟒𝟎𝟎
Y
𝟑𝟓
𝟖𝟎𝟎 Z
What is the measure of <Y?
C
Examples: Find each indicated measure.
X
<X=___
K
KL=___
<Z=___
𝟐𝟑
𝟕𝟎𝟎
Y
M
L
Z
E
Q
F
<F=___
QR=___
P
𝟕
R
G
Examples: Find each indicated measure.
B
H
<ABD=___
GH=___
J
A
𝟔𝟓𝟎
𝟏𝟐
D
G
Y
𝟏𝟐𝟖𝟎
X
<X=___
Z
F
Examples: Find each indicated measure.
<T=___
U
8x
T
6x
V
Examples: Find each indicated measure.
D
𝟓𝟐
𝟎
𝟎
(𝟒𝒙 − 𝟖)
F
<F=___
<E=___
E
If EF = 3x-12 then ED = ___
Examples: Find each indicated measure.
X
W
XZ=___
𝟐𝟒
Y
𝟑𝟖
Z
Examples: Find each indicated measure.
L
<N=___
(𝟑𝒙 − 𝟕)𝟎
N
(𝟐𝒙 + 𝟏𝟒)𝟎
M
Examples: Find each indicated measure.
x=___
AC=___
y=___
B
BC=___ <A=___
8
A
C
Homework: Practice
Worksheet
Recall that the Polygon Congruence Postulate
states that if two triangles are congruent then
their corresponding parts are congruent.
E
B
A
If ∆ABC ≅ ∆DEF then:
D
C
F
This idea is often stated in the following form:
Corresponding Parts of Congruent Triangles are
Congruent, abbreviated as CPCTC.
Given: --------
------Prove: ----------
STATEMENTS
REASONS