Download File - Geometry

Geometry
Notes 4.6
Isosceles, Equilateral and
Right Triangles
Name:
Hour:
Lesson Goal: By the end of this lesson, you will be able to:
Use properties of isosceles and equilateral triangles to show angle measures, side lengths,
and prove triangle congruence.
Use properties of right triangles to show angle measures, side lengths, and prove triangle congruence.
- Prove triangle congruence using the Hypotenuse-Leg (HL) Theorem.
-
-
Draw and label an ISOSCELES triangle with the following:



Vertices A, B & C
Legs
Base


Base Angles
Vertex Angles
BASE ANGLES THEOREM: If
of a triangle are
the
opposite them are
CONVERSE OF THE BASE ANGLES THEOREM: If
are
, then
.
of a triangle
, then the
opposite them are
.
Both of these statements are TRUE, so we can write this in the form of a
statement!
THEOREM: Two
of a triangle are
opposite them are
if and only if the
.
Example 1:
Use the diagram of ∆ABC to prove the
Base Angles Theorem.
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅
GIVEN: In ∆ABC, 𝐴𝐵
̅̅̅̅ is the bisector of BAC
𝐴𝐷
PROVE: B ≅ C
An
Statements
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
triangle is a special type of an isosceles triangle.
If a triangle is EQUIANGULAR, then it is
.
If a triangle is EQUILATERAL, then it is
.
Example 2:
Find the value of x and y.
y
Reasons
So far we have learned about four ways to prove that triangles are congruent.

SSS (
) Congruence Postulate

SAS (
) Congruence Postulate

ASA (
) Congruence Postulate

AAS (
) Congruence Postulate
There is ONE MORE WAY to prove triangle congruence. This way is SPECIAL because it can only be used when
working with
triangles.
HYPOTENUSE-LEG (HL) CONGRUENCE THEOREM:
Let’s practice figuring out which congruence theorem we should use with some examples!
Congruence Theorem:
Congruence Theorem:
Congruence Theorem:
Congruence Theorem:
Congruence Theorem: